MULTI-BEAM CYCLOTRON-RESONANCE MASER ARRAY

TEL-AVIV UNIVERSITY 

THE IBY AND ALDAR FLEISCHMAN FACULTY OF ENGINEERING 

MULTI-BEAM CYCLOTRON-RESONANCE MASER ARRAY 

By 

Li Lei 

THESIS SUBMITTED FOR THE DEGREE OF “DOCTOR OF PHILOSOPHY” 

SUBMITTED TO THE SENATE OF TEL-AVIV UNIVERSITY 

February 2002

TEL-AVIV UNIVERSITY 

THE IBY AND ALDAR FLEISCHMAN FACULTY OF ENGINEERING 

MULTI-BEAM CYCLOTRON-RESONANCE MASER ARRAY 

By 

Li Lei 

THESIS SUBMITTED FOR THE DEGREE OF “DOCTOR OF PHILOSOPHY” 

SUBMITTED TO THE SENATE OF TEL-AVIV UNIVERSITY 

This Research Work was Carried Out at Tel-Aviv University 

in The Faculty Of Engineering 

Under The Supervision of Prof. Eli Jerby 

February 2002 

II

This thesis is dedicated to my parents, 

Lei Mao-Fan and Yin Shou-Lan 

III

ACKNOWLEDGMENTS 

I would like to express my sincere gratitude to my advisor Prof. Eli Jerby for his help, 

guidance, encouragement and support, sharing with me his insights, knowledge and 

experience throughout this work. 

Particular thanks to Dr. A. Fisher and Dr. D. Hinshelwood from the Naval Research 

Laboratory for their help on the cathodes issue. 

A helpful and pleasant association with Mr. M. Korol, Mr. A. Shahadi, Mr. A. Kesar, 

Mr. M. Bensal and Mr. Y. Reshef at Tel-Aviv University over the years is also gratefully 

acknowledged. 

IV

Contents 

Abstract------------------------------------------------------------------------------------------VII 

List of Abbreviations---------------------------------------------------------------------------IX 

Chapter 1. Introduction 1 

1.1. Cyclotron Resonance Masers---------------------------------------------------1 

1.2. The Concept of the Multi-beam CRM-array---------------------------------12 

1.3. Electron Emitters----------------------------------------------------------------18 

1.4. Thesis Outline--------------------------------------------------------------------24 

Chapter 2. 2D CRM-Array Experiment 25 

2.1. Experimental Design and Setup-----------------------------------------------25 

2.1.1. Electron Beams-----------------------------------------------------------29 

2.1.2. Magnetic Fields----------------------------------------------------------32 

2.1.3. Pulsed Power Devices---------------------------------------------------34 

2.1.4. The Periodic Waveguide------------------------------------------------36 

2.1.5. Vacuum System Considerations---------------------------------------40 

2.1.6. RF Diagnostics-----------------------------------------------------------40 

2.2. Experimental Operation---------------------------------------------------------42 

2.3. Experimental Results------------------------------------------------------------44 

2.4. Analysis and Discussions-------------------------------------------------------55 

2.5. Conclusions-----------------------------------------------------------------------58 

Chapter 3. The Carbon-Fiber CRM-Array Experiment 59 

3.1. Experimental Design and Setup------------------------------------------------59 

3.1.1. Mechanical Design-------------------------------------------------------61 

3.1.2. Multi-beam Carbon-Fiber Cathode Arrays---------------------------64 

3.1.2.1. Experimental Configuration---------------------------------64 

3.1.2.2. Cathode Fabrications-----------------------------------------66 

3.1.2.3. Electron Trajectories------------------------------------------67 

V

3.1.2.4. Power Supplies -----------------------------------------------69 

3.1.2.5. Electrical Performance---------------------------------------72 

3.1.3. Magnetic Fields----------------------------------------------------------79 

3.1.4. The Periodic Waveguide------------------------------------------------81 

3.2. Experimental Operation---------------------------------------------------------84 


3.4. Discussions-----------------------------------------------------------------------92 

Chapter 4. Conclusions 94 


4.2. Suggestions for Future Work---------------------------------------------------95 

Appendix A. Computer Programs and Simulations Documentation 96 

A1. The EGUN Code Simulation for the 2D CRM-Array Experiment--------96 

A2. The Magnetic Fields Calculation for the 2D CRM-Array Experiment---99 

A3. The EGUN Code Simulation for the Carbon-Fiber CRM-array 

Experiment-----------------------------------------------------------------------101 

A4. The Magnetic Field Calculation for the Carbon-Fiber CRM-array 

Experiment-----------------------------------------------------------------------105 

Appendix B. Circuits of the Pulsed Power Devices 108 

B1. Circuit of the Gun-Solenoid Pulser-------------------------------------------108 

B2. Circuit of the Kicker Pulser---------------------------------------------------109 

B3. Circuit of the Multi-Channel Gun Pulser------------------------------------110 

Appendix C. The Modified Marx Generator 111 

C1. Model 615 MR Pulserad------------ ------------------------------------------111 

C2. The Modified Model 615 Pulserad-------------------------------------------112 

References 113 

VI

Abstract 

The cyclotron-resonance-maser array (CRM-array) proposed by Eli Jerby is a novel 

device in which separate electron beams perform, simultaneously, a cyclotron interaction 

with a single Bloch wave in an artificial lattice. It consists of CRM elements coupled 

together under a common magnetic field. The CRM-array has the capability to generate 

high-power microwave with relatively low-voltage electron beams. The low-voltage 

operation reduces the system overhead and leads to a relatively compact device. The 

CRM-array may radiate directly to free-space as an active phased-array antenna. 

Furthermore, the phase of each element output, and therefore the antenna far-field 

radiation pattern, can be varied by the electron-beam voltages. 

This thesis presents experimental studies of the multi-beam CRM-arrays. In the 

present study, our effort focuses mainly on the establishment of the experimental 

fundamental frame of the multi-beam CRM-arrays. In addition, a secondary objective of 

the research was to explore a multi-beam CRM device with cold cathode arrays and to 

develop an efficient, reliable and cost-effective multi-beam electron source for vacuum 

electronic devices. This thesis describes the first successful operation of a two-beam 

CRM-array experiment. The experimental results verify the feasibility of the CRM-array 

concept and promote the efforts toward the realization of large CRM-arrays. 

A 2D CRM array was operated with one and two electron beams (~ 10 keV / 0.1 A 

each). Microwave output signals are observed in frequencies around 7 GHz in an axial 

magnetic field of ~3 kG. Spectral measurements of the CRM outputs reveal frequency 

sweeps along the CRM pulses. These are associated with electron energy variations, in 

accordance with the theoretical CRM tuning condition. The synchronism of the cyclotronresonance 

interaction with a backward spatial harmonic is confirmed. 

This thesis presents also a first demonstration of a multi-beam CRM scheme with 

cold-cathode arrays. Based on commercial carbon fibers, a multi-beam cold-cathode array 

VII

demonstrates ~400 µs pulses of ~0.1 A in each channel with two accelerating stages. By 

using this gun, the device operates at low voltages ~5 kV with ~0.4 ms pulse duration. 

Clear bursts of RF oscillations were observed around 5 GHz in the experiment. The CRM 

tuning results indicate clearly interactions with backward waves. The experimental results 

show that it is possible to use cold-cathode arrays instead of thermionic-cathode arrays in 

future multi-beam CRM devices. 

VIII

List of abbreviations 

2D - Two Dimensions 

3D - Three Dimensions 

B.P.F - Bandpass Filter 

BWO - Backward Wave Oscillator 

CARM - Cyclotron Auto-Resonance Maser 

CsI - Cesium Iodide 

CRM - Cyclotron Resonance Maser 

EEE - Explosive Electron Emission 

FEL - Free Electron Laser 

Eq. - Equation 

H.P.F - High Pass Filter 

HPM - High Power Microwave 

IF - Intermediate Frequencies 

LO - Local Frequencies 

MBK - Multiple-Beam Klystron 

OBK - One-Beam Klystron 

PC - Personal Computer 

PWC - Periodic Waveguide Cyclotron Resonance Maser 

RF - Radio Frequencies 

SCR - Silicon Controlled Rectifier 

SF6 - Sulfur Hexafluoride 

TWT - Travelling Wave Tube 

IX

Chapter 1 

Introduction 

Driving by the emerged new technologies and the potential applications, the 

innovative high-power microwaves sources have been developed rapidly in recent years. 

This chapter describes the motivation for the present work on multi-beam cyclotron 

resonance maser arrays, and provides a brief review of relative fields. An outline of the 

thesis is presented in Section 1.4. 

1.1. Cyclotron Resonance Masers 

The cyclotron resonance masers (CRMs) [1] are the high power microwave sources, 

which are based on the induced cyclotron instability of a transiting electron beam. A 

simplified CRM scheme is shown in Fig. 1.1a. The electron beam is guided by a uniform 

axial magnetic field B0. Initially, the electrons undergo a cyclotron motion, and they are 

uniformly arranged in rotational phase on a circle (see Fig. 1.1b). Their Larmor radius is 

r0L=v0⊥/ωc, where v0⊥ is the electron initial perpendicular velocity, and ωc = eB0/γ0m0 is 

the cyclotron frequency. Here γ0=(1-v0 2 /c 2 ) -1/2 is the relativistic factor and m0 is the rest 

mass of the electron. After the interaction with the electromagnetic (em) field, some of the 

electrons are decelerated in the electric field, rotate faster, and hence accumulate phase 

lead while others are accelerated, rotate slower and accumulate phase lag. Then, a phase 

bunching occurs and the electrons radiate coherently. As the electrons gain or lose energy 

from the transverse electric field, the change in the relativistic factor γ0 produces a 

corresponding change in the cyclotron frequency. Simultaneously, another phase 

bunching process occurs due to the Weibel mechanism that is the result of the axial 

Lorentz force. The two processes are always operating against each other. The cyclotron 

resonance satisfies the condition: 

ω = n ω + k v 

(1.1) 

c 

1 

z 

z

E⊥ 

ω, kz 

B0 

B⊥ 

(a) 

E⊥ 

(b) 

Fig. 1.1. The CRM interaction, (a) a schematic diagram, and (b) the process of the phase 

bunching (the white dots represent the electrons’ position at the time, t, and the red dots 

represent the electrons’ position at the time, t+∆t). 

2 

B0

where ω and kz are the em wave frequency and its wavenumber, respectively, ωc and vz 

are the electron cyclotron frequency and axial velocity, respectively, and n is the 

cyclotron harmonic order. 

In fast-wave devices, the phase velocity is higher than the speed of light in vacuum, 

vph>c, and the basic mechanism of radiation is the electron bunching under the influence 

of the transverse electric field component. The dominant effect in the fast-wave devices is 

the relativistic azimuthal bunching caused by the v⊥•E⊥ product, where v⊥ is the electron 

transverse velocity, E⊥ is the transverse electric component. In the slow-wave devices, the 

phase velocity is slower than the speed of light in vacuum, vph

CRMs have been developed and studied mainly in single electron-beam schemes [8]. 

Fast-wave devices such as gyrotrons, cyclotron autoresonance masers (CARMs), and 

slow-wave devices such as dielectric-loaded CRMs have been studied intensively. 

Dispersion diagrams for gyrotrons, CARMs and dielectric-loaded CRMs are illustrated in 

Fig. 1.2. The uncoupled waveguide mode in Fig. 1.2a, b is represented by 

2 2 2 2 

ω = ω c 0 + k z c 

(1.3) 

where ω c0 

is the cutoff frequency of the operating mode. The cyclotron wave in the 

electron beam obeys Eq.1.1. 

Both gyrotrons and CARMs operate through a fast cyclotron wave interaction. For 

gyrotrons, the interaction takes place near the electron cyclotron frequency ωc (Fig. 1.2a) 

where the CARMs interaction takes places with a phase velocity closed to the speed of 

light, as shown in Fig. 1.2b. In Fig. 1.2c, the dispersion function of the uncoupled 

waveguide mode is determined by the geometry of the waveguide, its dielectric 

properties, the frequency ω, and the wavenumber k. The Weibel interaction takes place 

slightly below the speed of light line and the synchronism occurs over a wide bandwidth. 

Various CRMs are based on the normal Doppler effect. The resonance occurs when 

the operating frequency ω is larger than the Doppler term kzvz, which means that the 

phase velocity, vph= ω/kz , is larger than the electron axial velocity vz. This corresponds to 

positive cyclotron harmonics (n>0, see Eq. 1.1). The radiating electrons lose both orbital 

and axial momentum components. The anomalous Doppler effect occurs when the 

operating frequency ω is smaller than the Doppler term kzvz, i.e. vph

(a) 

(b) 

(c) 

Gyrotron interaction 

Waveguide mode 


ωc 

ωc0 

ωc 

ωc 

Fig. 1.2. Dispersion diagrams for (a) gyrotrons, (b) CARMs, and (c) slow-wave CRMs. 

5 

ω 

ω 


c 

c 

Fast cyclotron mode 

beam line 

CARM interaction 

Fast cyclotron mode 

beam line 

kz 

kz 

ω 

Slow wave CRM interaction 

Slow wave CRM interaction 

c 

Slow cyclotron mode 

beam line 

kz

A gyrotron system usually consists of several distinct elements: a magnetron injection 

gun, an interaction region, a collector region and a strong externally applied magnetic 

field [14]. The electron beam is emitted from the electron gun, propagates along the 

interaction region, interacts with the em wave, and is deposited finally in the collector. 

In the gyrotron device, the transverse velocity of electrons in a helical beam via 

relativistic instability generates the high power RF. The change of the electron cyclotron 

frequency due to the relativistic electron mass variation causes phase bunching in the 

electron beam and, consequently, electromagnetic cyclotron instabilities [15]. 

Scientists at Gorky State University (former USSR) developed the gyrotron concept 

into a practical radiation source during the 60’s and 70’s. In 1975, they developed a 22 

kW CW oscillator that produced 2mm radiation with 22% efficiency [15]. In the 70’s 

there were also major advances in the United States at the Naval Research Laboratory 

(NRL) as well as at MIT, Yale University, Varian and Hughes. 

Gyro-devices, like linear-beam devices, have many variants. A full description of 

these devices is outside the scope of this work, but a list of the major types and schematic 

drawings of most important conventional linear-beam devices and their equivalent gyrodevices 

are presented in Table 1.1. For more detail see, for example Ref. [16]. 

Existing or potential applications of gyro-devices include plasma heating and current 

drive for nuclear fusions, RF acceleration in high-energy linear colliders, enhanced radar 

systems, and processing of material [17]. In past several decades, common experimental 

features of gyro-devices are focused on high average-power gyrotrons and high peakpower 

pulsed gyrotrons. 

High average-power sources of 100-500 GHz radiations are necessary for electron 

cyclotron heating of fusion plasmas. The configurations of electron cyclotron masers with 

open quasi-optical resonators, such as the quasi-optical gyrotrons, show considerable 

promise for operation in this wavelength regime with high power RF. 

6

Cathode 

(a) 

Solenoid 

(b) 

(c) 

Electric field 

for TE01 mode 

Circular waveguide 

Fig. 1.3. Schematic diagrams of a gyrotron (a), the magnetic field 

profile (b) and the beam-cavity cross section in the interaction 

region for a circular TE01 operating mode (c) [Ref. 14]. 

7 

B0z 

Collector 

Cavity 

Electron beam 

cross section 

z 

Typical electron 

cyclotron orbits 

RF output

In these configurations, the resonator mirrors are far from the beam-wave interaction 

region, which will allow a large volume for the interaction and low-ohmic heating 

densities on the mirrors. In addition, there is an effective control of transverse modes in 

the resonator, and separated electron-beam collection and RF output simplifies the 

development of depressed collectors. Table 1.2 presents a summary of the recent status of 

high frequency gyrotron oscillators for electron cyclotron resonance heating and current 

drive in nuclear fusion [18]. 

Using a pulse-line accelerator, an early 1 GW super-radiant oscillator experiment was 

reported by Granatstein et al. at 8 GHz [19]. Since the late 1970’s, a number of significant 

experimental results were reported for relativistic gyrotrons in USSR. These experiments 

have yielded tens of megawatts peak power at centimeter and millimeter wavelengths 

regime. Recently, the whispering-gallery gyrotrons have produced several hundred 

megawatts peak power of microwaves near 35 GHz in the Naval Research Laboratory 

(NRL) [20]. 

According to theoretical studies, gyrotrons may also have a high efficiency at high 

harmonics of the gyrofrequency. Thus interaction at high cyclotron harmonics becomes 

especially advantageous when large magnetic fields should be avoided [21]. At Fukui 

University, Japan and University of Sydney, Australia, the gyrotron have been operated 

successfully in single mode at the second and third harmonic of the electron cyclotron 

frequency [22-28]. The medium power and submillimeter gyrotron has achieved 

frequency tunability in a wide range, from 38 GHz to 850 GHz. 

Since the CARM was first suggested by Petelin [29] in 1974, several CARM 

experiments have been conducted at the Institute of Applied Physics in USSR [30-33], 

and at MIT [34, 35]. Recently, a CARM experiment with 26% high-efficiency at 7.9 mm 

wavelength was reported by Bratman et al. [36, 37]. Unlike the gyrotron, the CARM uses 

a large Doppler up-shift of the cyclotron frequency in order to reach high output 

frequencies [38, 39], and operates with vph~c. 

8

Table 1.1. Schematics of linear beam devices and corresponding gyro-devices [15]. 

Linear 

beam 

devices 

Gyrodevices 

Monotron Klystron TWT BWO Twystron 

Gyro- 

Monotron 

Gyro- 

Klystron 

Table 1.2. Present development status of high frequency gyrotron oscillators [18]. 

Frequency Power Period Efficiency 

Institution/State (GHz) (MW) (s) (%) 

CPI/US 110 0.68/0.53/0.35 0.5/2/10 31/30/27 

JAERI+Toshiba/Japan 110 0.35 5 30 

GYCOM/Russia 110 0.70/0.32 2/5 37/30 

Euratom Team/Europe 118 0.5/0.45 1/5 28/25 

GYCOM/Russia 140 1/0.65 1/2 >40 

GYCOM/Russia 140 0.8 1 50 

GYCOM/Russia 160 0.5 0.7 30 

JAERI+Toshiba/Japan 170 0.52/0.23 0.6/2.2 32 

9 

Gyro- 

TWT 

Gyro- 

BWO 

Gyro- 

Twystron

The CARM interaction is based on the same instability mechanism as that of the gyrotron, 

but it is operated much above cutoff frequency. The large Doppler frequency upshift 

permits a considerably reduced magnetic field B0. Therefore the CARM can provide 

millimeter and submillimeter radiation in the first electron-cyclotron harmonic using 

currently available magnet technology. In contrast to the gyrotron, which requires an 

electron beam with a large momentum pitch angle (typically α=v⊥/vz>1), the CARM has 

an electron beam with low to moderate pitch angle (α

unified description of CRM dynamics. This theory was further extended to the nonlinear 

range by Sprangle and co-workers [52, 53]. In 1980, Chu et al. applied kinetic theory to 

TE modes in cylindrical waveguides [54]. This method was extended later by Lau [55] 

and Fliflet [56] to TE and TM waveguide modes. The present status of the theory of 

cyclotron masers with relativistic electron beams is reviewed in [57]. 

Azimuthal bunching 

V⊥•E⊥ 

CRM devices 

Fast-wave devices Slow-wave devices 

CARM Gyrotron 

PWC Dielectric-loaded CRM 

Normal Doppler 

Vph>Vez 

Fig. 1.4. CRM effects and devices. 

11 

Axial bunching 

V⊥×B⊥ 

Vph~c Vph>c Vph

1.2. The Concept of the Multi-beam CRM-array 

CRM devices have a number of potential scientific, industrial and military 

applications. In particular, they are expected to be widely used as major sources of HPMs 

in future applications, such as material processing, nuclear reactors, radars, accelerators, 

and others. CRM’s and gyrotrons have been developed so far as single electron-beam 

tubes. In order to obtain high output power, the sole electron-beam should possess 

sufficiently large kinetic energy and current. Consequently, a major part of the overhead 

in a typical CRM system is devoted to peripheral accessories needed to maintain the 

powerful electron-beam itself, both in acceleration and collector sections. In fact, most of 

the total length of a typical gyro-device is devoted to the consequent overhead (including 

the high-voltage electron gun and electron-optics, the tube shielding, a long collector, and 

the output window). Those contribute to weight and high cost. Therefore, the search for 

novel high-power microwave sources, which have low costs and compact sizes, is an 

attractive topic in this field. 

The concept of multi-beam CRM-arrays was proposed by Jerby et al. [58-60] as a 

compact version of the single-beam CRM schemes. The idea is based on employing the 

transverse dimension to reduce the requirements of high voltage supplies and cooling 

systems. In the CRM-array, separate electron beams perform, simultaneously, a cyclotron 

interaction with a single Bloch wave in an artificial lattice. The CRM-array has the 

capability to generate high-power microwaves with relatively low operating voltages. 

A theoretical analysis of the CRM-array [61, 62] predicts a considerable gain in a 

single mode. In this physical model, Maxwell’s equations and Vlasov equation are used 

to analyze the mechanism of the multi-beam CRM in the linear region. The multi-beam 

CRM-array gain-dispersion relation in Laplace s plane is given by the following matrix 

equation [61] 

2 

−1 

~ ^ ^ ^ ^ 

^ ^ ^ 2 

1 

^ ^ 

⎛ ⎞ ⎡ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎤ ⎛ 

A⎜ s⎟ 

= ⎢s⎜ 

sU 

− Θ ⎟ − Qk 

⎜ s⎟C 

k ⎜ s⎟Θ 

pk ⎥ ⎜ sU 

− Θ k 

⎝ 

⎠ 

⎢⎣ 

⎝ 

⎞ 

k ⎟ 

⎠ 2 ⎝ ⎠ ⎝ ⎠ ⎥⎦ 

⎝ ⎠ 

12 

2 

A 

0 

(1.4)

^ 

where the subscript k denotes the harmonic order, s= jsL(L 

is the interaction length) is 

the normalized Laplace wavenumber, and U is a unit matrix, respectively. The space- 

charge matrix Θ ^ 

represents the effect of the electron current density on the CRM 

pk 

^ 

coupling. The power-flow-matrix C 

⎛⎜ 

k ⎝ 

s 

⎞ ⎠ ⎟ describes the distribution of the em wave power 

among the different modes and their spatial harmonics. The diagonal tuning matrix is 

^ 

Θ k 

^ 

=θ nk 

^ 

, where θnk − L 

= 

⎛⎜ 

ω−ωc −βnk 

V 

⎞ 

0z 

⎟ 

⎝ 

⎠ 

V 

. The subscript n denotes the mode 

13 

− 

0z 

^ 

order. Q 

⎛⎜ 

k ⎝ 

s 

⎞ ⎠ ⎟ is the diagonal coupling matrix and is defined as 

^ − ^ ^ ⎛ ^ − 

− 

⎛ ⎞ ⎛ ⎞ 

⎞ 1 

^ ^ ^ ^ 

2 ⎛ 

⎞ 

Q ⎜ ⎟ = ⎜ − Θ ⎟ ⎜ − 

⎟ 

k s β ez sU 

k Z k β ez U + β e⊥ 

⎜k 

0 Z k − sU 

− β k ⎟ (1.5) 

⎝ ⎠ ⎝ ⎠⎝ 

⎠ 2 ⎝ 

⎠ 

^ 

where k0 = kL is the normalized wavenumber, β ^ 

k and Z ^ 

k 

harmonic wavenumber and impedance, respectively, and β − 

are diagonal matrices of the 

ez 

and β− 

average normalized axial and perpendicular velocity components, respectively. 

e ⊥ 

are the electron 

This linear analysis shows the possible mode selectivity and spectral purity of the 2D 

CRM-array. These stem from the spatial filtering in the periodic structure. In addition, the 

CRM-array may have unique features of an active phased array antenna [63]. The 

immediate integration proposed, of a microwave generator combined with an antenna, 

may simplify the overall radiative system in many applications. 

Other types of microwave generators with more than one electron-beam have been 

proposed and studied by other workers [64-76]. These include the multiple-beam klystron 

(MBK), the multi-beam stagger-tuned gyroklystron, and the double-stream cyclotron 

maser. Most of them are in the stage of theoretical study except MBK. Several 

experimental schemes are under construction.

The concept of the MBK appeared in France in the 40’s [64], and this kind of MBKs 

has really exploited in USSR. In recent years, MBKs are under consideration in other 

countries such as US and China. They have shown that the use of multiple-beam designs 

provides a powerful means for improving the parameters of microwave tubes. The MBKs 

provide low operating voltages, high power, low noise, and the possibility of wider 

operating bandwidth by the increase in total perveance. Many models of MBKs are 

produced in Russia and most of them for radar and communication applications. 

However, only a small number of them are widely known and few details were appeared 

in open publications [65]. According to Russian’s work, as the beam number grows, the 

decreases of the characteristic impedance of the resonator are slower than the increases of 

the overall conductance of the multiple-beam due to the smaller contribution of the side 

capacitance. Therefore, for a MBK and an OBK (one beam klystron), in the case of 

equality of beam powers, beam perveances, and normalized radii of the channels, the 

MBK bandwidth is 2-2.5 times more than that of the OBK [66]. Two 6 cavity, 36 beams 

MBKs produce a total RF output peak power of 500-1000 kW with 60A beam current and 

a 28-34 kV beam voltage at the State Research and Production Corporation “ISTOK” in 

Russia [67]. The MBKs at 0.425, 0.85, 1.3, and 2.8GHz are also under development at 

Thomson Tubes Electroniques [68, 69]. The 1.3 GHz prototype operates with seven 133 

A beams and a 115 kV beam voltage. It produces a total RF output peak power of 10 MW 

with 65% efficiency. Meanwhile, researchers in the Institute of Electronics, Chinese 

Academy of Sciences (IECAS) focus on S-band and C-band MBKs [70]. In US, under the 

MURI program, several progresses are carried out at Stanford Linear Accelerator Center 

and University of California, Davis. In a W-band micro-fabricated modular klystrons 

scheme, the semiconductor’s deep-etch lithography technique is used. A klystron array is 

fabricated on single substrate. Several such modules can be stacked together to form a 

klystron “brick” and operated in parallel in order to produce high power RF by relatively 

low voltage. The “brick” can be driven by a single output, or by individual, spatially 

combined radiators [71]. 

Replacing the solid electron beams by hollow electron beams, a multi-beam 

gyroklystron was proposed by Nusinovich et al. A theoretical model of multi-beam 

14

stagger-tuned gyroklystrons was developed. Two-stage, two-, three- and four-beam 

gyroklystrons operating in a small-signal regime were considered in detail. The analysis 

shows that when a number of beamlets is greater than or equal to four, it is preferable to 

stagger tune eigenfrequencies of individual input cavities around the eigenfrequency of 

the common output cavity. The simulation results demonstrate that the gain-bandwidth 

product in multi-beam gyroklystrons can be increased due to the stagger tuning much 

more stronger than in their single-beam counterparts [72]. 

The double-stream cyclotron maser was proposed by Bekefi at MIT [73]. In this 

scheme, two well-intermingled electron beams of different axial velocities are spun up 

and allowed to gyrate in a uniform axial magnetic field. The spun-up beams interact in a 

cylindrical waveguide. Bekefi’s formulae show that the resonant frequency of the 

cyclotron double-stream interaction is proportional to the cyclotron frequency and is 

inversely proportional to the difference in the axial velocities of the beams. He predicts 

that the double-stream cyclotron maser can operate at high frequencies without the need 

of either high-beam voltage or high magnetic field. Later, a linear instability analysis of 

this maser was developed by Bekefi and his co-workers and the result of computer 

simulations shows that the cyclotron two-stream instability is primarily electrostatic [74]. 

A two-stream relativistic klystron amplifier and a high-power X-band relativistic twostream 

amplifier were proposed in a similar idea [75, 76]. The operating principle of these 

schemes is also based on the unstable interaction of the fast cyclotron space-charge wave 

on one electron beam and the slow cyclotron space-charge wave on other electron beam. 

The CRM-array was proposed by Jerby as an extension of the periodic-waveguide 

CRM scheme shown in Fig. 1.5a. In this device, referred here as a 1D CRM-array, the 

waveguide consists of metal posts in two columns, where the electron-beam flows in 

between them. Amplifier [46] and oscillator experiments [47] were conducted at X-band 

frequencies (8-12 GHz) with electron-beams of ~10 keV. The 1D-CRM oscillator yielded 

a coherent output of 0.4 kW power at >25% efficiency. Theoretical studies of 1D-CRM 

interactions with slow and fast waves are presented in [48]. A direct scale-up of this 1D 

scheme to high power levels might have required a system overhead comparable to that of 

15

similar single-beam gyrotrons. The preferred alternative was to increase the device 

dimensionality. 

Conceptual schemes of 2D and 3D CRM-arrays are illustrated in Figs. 1.5b and 1.5c, 

respectively. The CRM-array consists of many 1D CRM channels; each operates with a 

low-voltage, low-perveance electron beam. The different channels may be strongly 

coupled together through the waveguide lattice. Synergistic effects between these 

channels may increase the output power further. In order to compensate for any transverse 

non-uniformity in the magnetic field profile, each electron beam can be tuned to a slightly 

different accelerating voltage. 

The ultimate 3D CRM-array may consists of tens, and even hundreds electron beams. 

Advanced cathode arrays, made of carbon fibers, silicon tips, or ferroelectric ceramics, 

could be applicable in this device. The radiation output can be emitted from the exit plane 

of the CRM-array, directly to free-space. In more sophisticated schemes, the CRM-array 

may have features of an active phased-array antenna [63]. Focusing, steering, and 

splitting of the radiation lobe could be manipulated by varying the voltage profile across 

the cathode array. 

The major advantages expected for the CRM-array concept are: 

(a) Reduced power-supply size and weight. 

(b) Reduced X-ray radiation level due to the low-voltage operation. 

(c) Miniaturization due to the integrated magnet. 

(d) Reduced space-charge effects due to the separated low-current electron beams. 

(e) Spectral purity and mode selectivity determined by the lattice dispersion. 

(f) Direct radiation to free-space. 

(g) Direct energy radiation as a phased-array antenna, incorporated in the multi-beam 

CRM-array itself. 

The comparison of the single-beam high-power microwave source and the multi-beam 

CRM-array is summarized in Fig. 1.6. 

16

(a) 

(b) 

(c) 

B0 

B0 

B0 

metallic tube 

electron beam 

17 

electron beams 

metallic tube 

electron beams 

metal posts 

metal posts 

metallic tube 

metal posts 

Fig. 1.5. The evolution of the CRM-array concept: 1D, 2D, and 3D 

CRM-array schemes (a, b and c, respectively).

1.3. Electron Emitters 

There are several kinds of cathodes used in high power microwave devices. The most 

common cathodes are thermionic cathodes. Cold cathodes are also used. In this work we 

utilize both thermionic cathodes and cold cathodes. 

Thermionic Cathodes 

HPM Generation 

Single high energy e-beam Multi-beam CRM-array 

High voltage 

Large system overhead 

Need X-ray shielding 

High current 

Space charge effects 

Increase the spatial dimension 

Fig. 1.6. Single-beam vs. multi-beam HPM generation. 

Thermionic cathodes are based on thermionic emission mechanisms. Thermionic 

emission results from the heating of the cathode to provide the electrons with a sufficient 

kinetic energy to overcome the potential barrier (work function) at the surface and escape 

18 

Array of low-voltage 

Compact size, less X-ray 

Separated electron beams 

Less space charge effects 

Lattice dispersion 

Mode selectivity 

Beam steering 

“Active” phased array

into vacuum. The current density J is given by the Richardson-Dushman equation as 

follows [77]: 

2 ⎛ eφ 

⎞ 

J = A0 

T exp⎜− 

⎟ A/cm 

⎝ kT ⎠ 

2 (1.6) 

where k is the Boltzmann constant, φ is the work function, T is the absolute temperature 

in degrees Kelvin ( o K), and A0 = 1.20×10 6 A/cm 2 o K 2 . 

However, in the case of space charge limitation, the current density J is given by the 

Langmuir-Child equation [78, 79] 

−6 

3 / 2 

J = 2. 3× 

10 GV A/cm 2 (1.7) 

where V is the acceleration voltage in volts, and G is a quantity, given in cm -2 , which 

depends on the geometric configuration of the electrodes. In the simplest case of parallelsided 

electrodes, G=1/d 2 , d is the cathode-anode distance. From Eq. 1.6, it is clear that in 

order to obtain a strong emission, the work function φ must be low and the temperature 

Τ must be high. Because Barium has a low work function (1.8 eV) and a moderate 

melting temperature (850 0 C), Barium impregnated tungsten cathodes have been widely 

studied since their introduction in the early 50’s. The Philips B-type cathode developed 

by Levi [80, 81] in 1953 is still the most widely used cathode in the microwave tube 

industry. An improved version of the familiar impregnated cathode is the M-cathode [82], 

which employs a coating of an ally of platinum group metals on the emissive surface to 

lower the work function of the activated cathode. Then this emitter may be operated at 

lower temperatures than the standard dispenser cathode for the same current density and 

has significantly longer operating lifetime. More recently, new types of cathodes have 

been investigated, for instance, a variety of versions of the impregnated dispenser cathode 

is distinguished by the composition of the impregnation or by the substrate type [83]. 

Cold Cathodes 

The current density of conventional thermionic cathodes is limited to the order of 10 

A/cm 2 [84]. For ultra high power microwave generation, a larger current density is 

required. In addition, direct modulation of the emitted beam can improve the efficiency 

19

and reduce the size of the microwave source. Thus various cold cathodes have been 

developed over the years to meet those desires. 

Cold cathodes do not rely on the heating of a material to emit electrons over the 

potential barrier. One of the most common types of cold cathodes is the field emitter, 

which is based on field emission. Field emission is the process whereby electrons tunnel 

through a barrier in the presence of a high electric field. Fowler and Nordheim developed 

a model describing the emission of electrons from a metal-vacuum interface in the 

presence of an electric field normal to the surface [85]. Their theory predicted that the 

current density of the field emission can be expressed as 

C 

J = 2 

φt 

( y) 

E 

2 

3 ⎛ 

⎜ 2 Bφ 

v 

exp⎜ 

− 

⎜ E 

⎝ 

20 

( y) 

⎞ 

⎟ 

⎟ 

⎟ 

⎠ 

A/cm 2 (1.8) 

where E is the applied electric field, φ is the work function, C and B are constants, 

3 2 

y = e E φ , and v(y) and t(y) are tabulated functions which arise due the inclusion of 

image charge effects. 

Dyke and Dolan have recognized the advantages of field emission as a highbrightness 

electron source in the 50’s. They discovered that to ensure stable emission and 

long life on tungsten field emitters, the ultra-high vacuum is required [86]. Later, the 

group at Stanford Research Institute (SRI), lead by Spindt, has developed the gated field 

emitter arrays (FEAs) successfully using micro-fabrication technology [87]. The Spindttype 

FEAs become one of the most common structures for field emission cathodes. The 

“Spindt cathode” is illustrated in Fig. 1.6. In the Spindt structure, the electrons are 

generated from very sharp molybdenum tips and an electron gate electrode is used to low 

the necessary operating voltage in order to produce a large electric field at the tips. 

Despite the variety of techniques and material, this kind of FEAs has been developed 

successfully as commercial flat panel displays, field emission displays (FEDs). Since 

FEDs have almost 180 degrees viewing angle, excellent color reproduction, flatness and 

low power consumption, it looks very promising.

There are many other types of cold cathodes, such as photocathodes, ferroelectric 

ceramic cathodes and explosive electron emission cathodes. We will describe more in 

detail the latter one in the following sections since this work has used carbon-fiber 

cathodes. For more details on other cathodes see, for example, the review article by 

Nation et al. [88]. 

Vanode 

Vgate 

Fig. 1.6. Schematic of Spindt-type field emitter array. 

Compared with field emitters, when the electric field is high enough, ohmic heating of 

the discrete electron emission sites will explode the cathode to vaporize and subsequent 

plasma formation by electron neutral collisions. There is also plasma formation on the 

anode, and diode gap closure occurs as the two plasma fronts expand. This process is 

known as explosive electron emission [88]. 

In USSR, Mesyats’ group has made since the mid 1960’s an extensive research on the 

processes of plasma formation and intense electron beams involved microscopic point 

emitters at high current densities emission. According their report, the work behavior of 

the explosive single emitter has four stages [89, 90]. Initially, followed a rapid rise in 

current a field emission current is observed after some delay by an explosive destruction 

21 

Anode 

micro tip 

gate electrode 

substrate

of the emitter. Simultaneous with the beginning of the current rise, a cathode flare appears 

on the cathode. Then, the current rises slowly, which is attributed to a decrease in the 

impedance due to plasma expansion. Later, an anode flare appears and the diode 

impedance collapses, simultaneous with a rapid current increase. The breakdown time, 

τδ , is related to the plateau current, j, by j 2 τδ=constant. Here j strongly depends on the 

electric field, so does τδ . If the explosion is initiated by field-emission current, the 

Fowler-Nordheim equation gives a good agreement with these single emitter experiments. 

Focused on broad area cathodes, Parker and coworkers at the Air Force Weapons 

Laboratory studied in the 70’s the electrical behavior of graphite cathodes. They 

considered that the observed diode perveance can be explained in terms of the expansion 

of the plasma cathode formed by the merger of many cathode flares [91]. The exact 

mechanism for broad area cathodes is not yet known; none of the theories so far proposed 

can explain all of the experimental results. However, the pre-breakdown and breakdown 

currents in a broad area cathode are observed to occur at electric fields about 10-1000 

times lower than those in a single needle emitter [92]. The effect of gap closure may limit 

the performance of devices operating with cold-cathodes, since it limits the duration of 

the electron-beam pulse, and precludes operation at desired repetition rates [93]. 

Impedance collapse characterized by the speed of the gap closure is roughly constant over 

a wide range of conditions at values of about 10 6 cm/s. Because of the gap closure, most 

of the cathodes used limit the pulsed duration to about 100’s ns. In order to prevent the 

breakdown, most studies in the cold cathodes use short pulse. It is useful, therefore, to 

develop new kinds of cold cathodes or processes, which the pulse lengths can be 

extended. 

Recently, the researchers at NEC Corporation in Japan have demonstrated a 

miniaturized traveling waveguide tube (TWT) results of 27.5 W at 10.5 GHz, 19.5 dB 

gain, and a bandwidth wider than 3 GHz using a lateral-resistor-stabilized Spindt-type 

FEAs [94]. Another TWT design by NEC, using a new arc-resistant vertical current 

limiter Spindt-type FEAs resulted an 8 W output power, 22 dB gain at 11.5 GHz and was 

stably operated for 5000 hours [95, 96]. The arc-resistant FEA appears to dramatically 

22

enhance the lifetime of the FEA cathodes in the vacuum environment and re-energize the 

efforts of researchers to develop high-power vacuum electronic devices based on cold 

cathodes. 

Carbon fibers are known for a long time as field emission sources [97-99]. In these 

early works, carbon fibers have been studied as pure field emitters, having been used 

singly and in clusters to provide DC emission without plasma formation. The 

experimental results have a good agreement with the Fowler-Nordheim equation. The 

emission characteristics and stability of these cathodes are, to a large degree, determined 

by the type of the carbon fiber microstructure, by the features of the manufacturing 

process, and by the initial treatment of the emitters. 

Further developments of carbon-fiber emitters with plasma formation in western 

countries were reported in the 80’s by Prohaska and Fisher. Using carbon yarn, emission 

starts at 5-15kV/cm and 10-30kV/cm, current densities up to 10A/cm 2 have been obtained 

over 100 cm 2 [100]. Researchers in New Mexico demonstrated that cloth fiber (75% 

rayon, 25% silk) cathodes might have superior properties as cold cathode emitters [101]. 

However for the broad area carbon-fiber emitters, the experimental results do not agree 

with the Fowler-Nordheim equation. Even with extremely careful diode design, the 

available pulse duration for any of the carbon felt, velvet, and high-grade graphite 

cathodes is usually limited by gap closure. The gap closure velocity depends most 

critically on the electrical field strength at the cathode surface, the cathode emissive 

material, and magnetic field [102]. Most recently, experiments on carbon-fiber emitters 

have tested the effect of CsI (Cesium Iodide) coated carbon-fiber cathodes [103, 104]. 

They have found that carbon-fiber cathodes coated with CsI did reduce the speed of the 

gap closure. In our laboratory, the single beam carbon-fiber cathode was demonstrated for 

1.2 ms current pulses [105], and was operated for a CRM experiment [106]. 

The carbon-fiber cathode is rarely used in microwave-tube experiments [107]. Since 

carbon has a high sublimation temperature (4×10 3 0 K), it has a long lifetime at current 

densities of >10 3 A/cm 2 [103]. In addition, such kind of material can easily be configured 

23

to provide multi electron beams in arbitrarily large diameter configurations. Therefore, in 

this study we use carbon-fiber cathodes to explore the operation of multi-beam coldcathode 

arrays for the CRM devices. 

1.4. Thesis Outline 

The thesis describes the experimental studies of the multi-beam CRM-arrays. At 

present, our studies focus mainly on the establishment of the experimental fundamental 

frame of the multi-beam CRM-array. A secondary objective is to explore multi-beam 

CRM devices based on the cold-cathode arrays, carbon-fiber cathode arrays, and to 

develop an efficient, reliable and cost-effective multi electron-beam source. 

In this thesis, Chapter 2 presents the first successful operation of a two-beam CRMarray. 

The spectral measurements were carried out with one and two-electron beam CRM 

devices. The chapter includes a detail description of the experimental setup, experimental 

operation, experimental results, and an analysis of the possible mechanism for the 

resonant microwave radiation observed. The first carbon-fiber CRM-array experiment is 

presented in Chapter 3. The multi-beam CRM scheme with cold-cathode arrays is 

demonstrated. This experiment illustrates the use of carbon-fiber emitters as electron 

sources in multi-beam CRM devices. Meanwhile, the study of the multi-beam carbonfiber 

cathode array is described intensively in this chapter. The conclusions of this thesis 

are summarized in Chapter 4. 

24

Chapter 2 

2D CRM-Array Experiment 

This chapter presents the first experimental study of a 2D CRM-array. The CRMarray 

operates with one or two electron beams. The next section describes the 

experimental design and setup. The operation of the experiment is described in Section 

2.2. The highlights of the experimental results in each case are presented in Section 2.3. 

Both, fast- and slow-wave CRM interactions are observed in the experiment. The spectral 

measurements show clearly the CRM interaction with backward spatial harmonics. The 

experimental results are analyzed and compared to the theory in Section 2.4. The 

conclusions are presented in Section 2.5. 

2.1. Experimental Design and Setup 

A photograph of the experimental setup of the 2D CRM-array is shown in Fig. 2.1. 

The oscillator tube consists of a planar multi-beam electron gun, a 2D periodic 

waveguide, a collector, a solenoid, and a kicker coil, which imparts initial transverse 

velocity to the electrons. The total length of the system is about one meter. 

A block diagram of the experimental setup is shown in Fig. 2.2. The CRM device is 

immersed in a uniform axial magnetic field (2-4 kG) and activated by pulsed power 

supplies. The electron beams are emitted from dispenser thermionic cathodes (Spectra- 

Mat, STD200, 5 mm diameter), spun up by the small kicker coil, and propagate in 

cyclotron motions along the periodic waveguide channels. The waveguide consists of a 

metal-post array with 4x24 elements and is terminated by half-period reflecting sections 

in both ends. The first row of metal posts acts as an anode. A waveguide taper at the end 

is used as a mode converter and also as a collector for the electron beams. In another 

scheme (not presented here) the collector is divided to each electron beam. The beam 

currents are measured by means of 10 Ω resistors. A small portion of the RF power is 

sampled by a 20 dB cross-coupler, and by three sampling probes mounted inside the 

25

waveguide. The output coupled RF signal is attenuated and divided into two arms. In one 

arm, the signal is detected by a high-sensitivity crystal detector and recorded by a digital 

oscilloscope (Tektronix TDS 540). In the other arm, the signal is fed into a mixer (HP 

5364A) and mixed with a local-oscillator wave generated by a synthesizer (HP 83752A). 

The heterodyne signal is analyzed by a frequency and time-interval analyzer (HP 5372A), 

which enables intra-pulse frequency variation measurements. The parameters of the 2D 

CRM-array experiment are listed in Table 2.1. The more detail design is given in the 

following sections. 

Fig. 2.1. Photograph of the experimental setup. 

26

electron 

gun 

vacuum pump 

pulsers RF diagnostics 

kicker 

solenoid 

Fig. 2.2. Schematic of the 2D CRM-array experimental setup. 

27 

Frequency-time 

analyzer 

synthesizer 

RF probes 

cathodes waveguide solenoid 

mixer 

attenuators 

oscilloscope 

detector 

10Ω 

RF coupling 

Collector 

and RF-load

Table 2.1. 2D CRM-array Experimental parameters. 

Electron beams: 

energy 4.0 - 10.5 keV 

beam current ~ 0.1 A 

pulse duration 0.2 ms 

beams 1 or 2 

Magnetic fields: 

solenoid 2.5 - 3.9 kG 

kicker ~ 0.7 kA turns 

Periodic waveguide: 

rectangular tube 48 × 22 mm 2 

length 48 cm 

post diameter 1.5 mm 

array size 4 × 24 

periodicity 20 mm 

28

2.1.1. Electron Beams 

A planar electron gun was used in this experiment. A sketch of the electron gun is 

shown in Fig. 2.3. In the two-beam CRM experiment, the two side cathodes shown in red 

color in Fig. 2.3 were used to generate electron beams; whereas, in the one-beam CRM 

experiments, all of them were used separately to generate an electron beam in individual 

experiment. The gap between anode and cathode is 6 mm. A 2 mm thick stainless steel 

was used to fabricate the anode. The anode has three 6 mm diameter holes in order to 

apply the multi-beam operation. The distance between two adjacent cathodes is 9.5 mm. 

The cathodes are STD200 dispenser thermionic cathodes (5 mm diameter) made by 

Spectra-Mat Ltd. In a later experiment, for the vacuum consideration, we removed this 

anode and used the first row of metal posts in the periodic waveguide as an anode. For a 

new cathode, the optimal filament voltage is approximately 8V and the heating power is 

around 40 W. 

cathodes 

Fig. 2.3. Sketch of the electron gun used in the 2D CRM-array experiment. 

The electron gun design was performed with the EGUN code [108] with a few 

assumptions. This code is designed to compute trajectories of charged particles in a 2D 

symmetry of electrostatic and magnetostatic fields, including the effects of space charges 

and self-magnetic fields. Starting options include Child’s Law conditions on cathodes of 

various shapes, as well as user specified initial conditions. In the 2D CRM-array 

experiment, we assumed: (1) each beam has a perfect local symmetry around its own 

axis, (2) each beam has the same electron flow, (3) the gap between cathode and anode is 

smaller than the distance between two holes in the anode. 

29 

anode 

cathode holder

R (mm) 

Current Density (0.0246 A/mm 2 ) 

Fig. 2.4. The EGUN code output for a 5mm cathode and 6mm gap with a tapered magnetic 

field: (a) the beam trajectory [radius (R) vs. axial length (Z)], (b) electron density vs. 

radius (R). 

30 

Z (mm) 

R (mm)

Fig. 2.4. (Cont.) The EGUN code output for a 5mm cathode and 6mm gap with a tapered 

magnetic field: (c) the angle of the electron motion measured from the z axis. 

Thus we simulated the center electron flow and simplified the boundary. The code output 

for a 5 mm cathode with 6 mm gap is shown in Fig. 2.4. Fig. 2.4a shows electron gun 

geometry and beam trajectory. It includes two regions: a cathode-anode region and a 

beam tunnel. Figs. 2.4 b, c presents electron density versus radius, and the angle of the 

electron motion measured from the z-axis. 

31 

R (mm)

2.1.2. Magnetic Fields 

In this experiment, we used a solenoid to provide an axial magnetic field for 

cyclotron motions. It was made out of a 2 mm diameter copper wire with 15 turns/cm. 

Similarly, a kicker was made out of a 1 mm diameter copper wire with 52 turns/cm. The 

cross section view of a round, finite, air core solenoid is shown in Fig. 2.5. 

by 

B 

z 

The magnetic field at any point on the axis of a finite solenoid is approximated [109] 

⎧ 

⎪ 

µ NI 

r + 

⎪⎛ 

⎞ 

= 

0 

l 2 

( z) 

k 

⎨⎜ 

z + ⎟ ln 

2( 

r − r ) l ⎪⎝ 

2 

2 1 

⎠ 

⎪ r + 

⎪ 

1 

⎩ 

2 

2 ⎛ l ⎞ 

r + ⎜ z + ⎟ 

r + 

2 ⎝ 2 ⎠ ⎛ l ⎞ 2 

− ⎜ z − ⎟ ln 

2 ⎝ 2 ⎠ 

2 ⎛ l ⎞ 

r + ⎜ z + ⎟ 

r + 

1 ⎝ 2 ⎠ 

1 

where Bz is the magnetic field, in Tesla, µ0 is the permeability constant (1.26×10 -6 H/m, 

for coils measured in meters). Ik is the current in Amperes. l, r1, r2, and N are the 

solenoid length, inner and outer radii, and the number of turns, respectively, The 

experimental parameters are shown in Table 2.2. In Fig. 2.6, the solid curve shows the 

magnetic field of the solenoid and the dashed curve shows the magnetic field of the 

kicker. The star sign indicates the front-end position of the cathodes. 

r2 r1 

Fig. 2.5. Solenoid in cross section. 

l 

32 

2 ⎫ 

2 ⎛ l ⎞ 

r + ⎜ z − ⎪ 

2 

⎟ 

⎝ 2 ⎠ ⎪ 

⎬ 

2 

2 ⎛ l ⎞ ⎪ 

r + ⎜ z − 

1 

⎟ ⎪ 

⎝ 2 ⎠ ⎪⎭ 

z B 

(2.1)

Table 2.2. The parameters of the solenoid and the kicker. 

Parameter Solenoid Kicker 

Turns 900 120 

Current [A] 100-200 20-140 

Inner radius r1 [cm] 5.15 5.5 

Outer radius r2 [cm] 6.3 6.5 

Length l [cm] 60 2.3 

* 

Fig. 2.6. The magnetic fields of solenoid (solid curve) and kicker (dashed curve). 

The star sign represents the start point of the electron beam. 

33

2.1.3. Pulsed Power Devices 

Three high-voltage pulsers were designed and built in order to run the CRM 

experiment. The three incorporate pulsers are used for the electron gun, solenoid, and 

kicker. Their electric circuits are shown in Appendices B1 and B2. An overview of the 

pulsers is shown in Fig. 2.7. Each of the pulsers consists of a low-voltage capacitor bank 

(C), an SCR control circuit which is used as a gate, a diode Dc which prevents a reverse 

recharging of the capacitor, and a transformer (car ignition coil). Fig. 2.8 shows 

schematically a principle configuration of a high voltage electron gun pulser [110]. In 

this scheme an electron gun serves as a load. The high-voltage secondary winding of the 

transformer is connected directly to the electron gun. The pulse length, the voltage, the 

maximum currents, and the load’s parameters determine the parameters of each pulser. 

Fig. 2.9 shows schematically a principle configuration of a high voltage solenoid pulser. 

Here high voltage comes out from charged capacitors directly. The homemade solenoid 

pulser generates a 650 V, 40 ms pulse that corresponds to a peak magnetic field of 3 kG. 

The electron gun pulse reaches 12 kV and its pulse width is around 0.4 ms. The kicker 

coil can produce 7 kG maximum magnetic field on axis. All three pulsers are triggered 

with an adjustable delay between them. The kicker and electron gun pulsers are triggered 

near the peak of the solenoid pulse as shown in the timing diagram in Fig. 2.10. The 

solenoid pulse has 40 ms duration. Comparing to the 0.4 ms duration of the electron gun 

pulse, the CRM operates in a closely constant magnetic field. The electron gun voltage is 

measured by a high voltage probe (Tektronix P6015A). The currents of the solenoid and 

the kicker are measured with a series 0.05 Ω resistors. 

Fig. 2.7. Overview of the homemade pulsers. 

34

control 

control 

Voltage [a.u] 

8 

7 

6 

5 

4 

3 

2 

1 

0 

SCR 

C 

Dc 

Fig. 2.8. Schematic of the electron gun pulser. 

SCR 

Dc 

Fig. 2.9. Schematic of the solenoid pulser. 

Gun 

-10 -5 0 5 

Time [ms] 

10 15 20 

35 

Kicker 

Solenoid 

Fig. 2.10. A timing diagram of the solenoid, kicker and electron 

gun pulsers. 

cathode 

electron gun 

solenoid 

anode

2.1.4. The Periodic Waveguide 

The periodic waveguide used in this experiment is illustrated in Fig. 2.11. The main 

part is a 60 cm long WR 187 waveguide welded with a 4×24 metal-post array. It is 

terminated by half-period reflecting sections in both ends. The first row of metal posts 

acts as an anode. 

It is well known that any periodic slow wave structure of N periods, when shorted 

appropriately at both ends, will exhibit (N+1) discrete resonant frequencies with phase 

shifts per period equally spaced between 0 and π. Generally speaking, these specific 

resonant modes can be determined experimentally and then used to fit a curve to give the 

complete dispersion function. Using the method described in Refs. [111, 112], the 

minima in the reflection trace present the resonance frequencies of the finite periodic 

waveguide, and satisfy the resonance condition 

φs = βsL=sπ, s=1,2 ... 24 (2.2) 

where φs is the phase shift, βs is the discrete wavenumber, and L is the waveguide length. 

The dispersion curve is constructed by the measured frequencies of the reflection minima 

and the discrete wavenumbers. 

The cavity resonances were measured with the reflection coefficient of the slow wave 

structure over the appropriate frequency range. The measured results at the first and 

second passbands are presented in Fig. 2.12 and Fig. 2.13, respectively. The curves show 

the measured resonant absorption peaks corresponding to 23 axial modes of the cavity. 

This was achieved by a scalar network analyzer (HP 8757A). The testing system setup is 

shown in Fig. 2.14. The waveguide dispersion (without electron beams) is shown as a 

Brillouin diagram in Fig. 2.15, as results from measurements of the waveguide reflection 

and transmission coefficients. The dots indicate the measurement points of the 2D 

periodic-waveguide. The dashed curve indicates the fundamental mode of the rectangular 

tube. 

36

(a) 

(b) 

(c) 

40 mm 

4×24 metal posts 

2×11.14 mm 

3×9.51 mm 

30 mm 

WR 187 choke flange 

φ 38 mm 

10 mm 

2 ¾ ″ flange 

welding 

20 mm 

600 mm 

Fig. 2.11. The periodic waveguide construction, (a) an overview, 

(b) a cross section view, and (c) a side view. 

37 

probes 

WR 187 waveguide 

WR 187 

choke flange

Fig. 2.12. The measured reflection curve at the first passband. 

Fig. 2.13. The measured reflection curve at the second passband. 

38

Frequency [GHz] 

14 

12 

10 

8 

6 

4 

2 

sweeper 

directional bridge 

Periodic waveguide 

Fig. 2.14. A block diagram of the testing system used for the 

measurement of the dispersion relation. 

-160 -80 0 80 160 

Wave number [1/m] 

Fig. 2.15. The measured Brillouin-diagram of the 2D periodic-waveguide (the dots 

indicate measurement points). The dashed curve indicates the fundamental 

mode of the rectangular tube. 

39 

HP 8757 A 

scalar network analyzer 

attenuator

2.1.5. Vacuum System Considerations 

In general, metals, ceramics, and some plastics, such as Teflon are satisfactory in 

systems having ultimate vacuums down to 5×10 -7 Torr. In this experiment, the main 

vacuum chamber is the periodic waveguide shown in Fig. 2.11. It connects with pump 

system through a 2 3 /4″ flange. The parts of feedthroughs and window are connected by 

O-ring type connectors. Generally, the tube is pumped down to a pressure less than 10 -6 

Torr by a Varian 20/l triode pump (model 911-5030). A Varian Turbo-V250 pump 

(model 969-9008) is used for rough pumping. Most of the time, the system will need to 

be baked to 100 0 C (since we have O-ring, this temperature can not be too higher). 

2.1.6. RF Diagnostics 

The details of the experimental diagnostic setup are shown in Fig. 2.16. The RF 

diagnostics can be classified into two aspects, power measurement and frequency 

diagnostic. For power measurements, a Schottky barrier diode is used to rectify and 

detect the envelope of a RF pulse, generating a nonlinear DC output in the instantaneous 

electric field. Then this DC output is recorded by a digital oscilloscope (Tektronix TDS 

540). A key factor to protect the detectors is the accurate attenuation of RF signals. Two 

methods of the frequency diagnostic are used, one based on the measurement by 

bandpass filters and the other based on the measurement by a frequency and time-interval 

analyzer (HP 5372A). A waveguide (WR 187) which has a cutoff frequency of 3.28 GHz 

is used. Afterward, two filters are used for a coarse survey of the frequency. Their 

bandpass are 5.68-7.45 GHz and 8.13-10.00 GHz, respectively. According to the coarse 

measurement of the frequency, a local signal (LO) from a synthesizer (HP 83752A) is 

selected. The LO signal is mixed with the RF output signal. Then the heterodyne IF 

signal is sent to the frequency and time-interval analyzer (HP 5372A) for the accurate 

frequency measurement. A power limiter is used to protect the frequency and timeinterval 

analyzer. All data are recorded and processed on-line with the aid of a PC. The 

communications are through GPIB interface cables and a HP VEE 3.0 software is used to 

collect data. 

40

cyclotron oscillator 

WR 187 waveguide 

DC block 

computer 

GPIB interface cable 

attenuator 

Tektronix TDS 540 oscilloscope 

RF out 

RF detector 1 

bandpass 

filter 

divider 

divider 

HP 5372A frequency and 

time-interval analyzer 

Fig. 2.16. The experimental diagnostic setup. It includes power 

measurement and frequency diagnostic. 

41 

power limiter 

RF detector2 

GPIB interface cable 

HP 5364A microwave 

mixer/detector 

RF 

IF 

L.O. 

HP 83752A 

synthesized sweeper

2.2. Experimental Operation 

Each experiment began with a warm-up period, typically a few hours, to activate the 

cathodes. Initially, the filaments were operated at a potential, of ~6 V. Then the potential 

was gradually increased to ~8 V in order to obtain the desired currents. For used 

cathodes, this potential has to be increased to 11 V. In the two-beam CRM experiment, 

we used two individual AC power supplies to heat the cathodes separately in order to get 

a uniform current in each beam. The AC supplies must isolate the electron gun voltage 

from the ground potential. The electron gun was adjusted to provide a 0.2 ms pulse at the 

desired current level (0.1-0.5 A). Typical voltage pulse of the electron gun and the beam 

current trace are illustrated in Fig. 2.17. The beam current was measured by a 

10Ω resistor placed between collector and ground. In the experiment, the periodic 

waveguide is connected to a ground potential, and the collector has to be isolated from 

the ground. 

The adjustment of the solenoid position, the calibrations of the diagnostic system, and 

cold measurements were conducted prior to each experiment. The desired uniform axial 

magnetic field was obtained by adjusting the solenoid position properly (the current trace 

in the collector should be clear), and by adjusting the peak level of the current pulse in 

the solenoid. Any directional change of the electron beams requires the re-alignment of 

the solenoid. 

The experiment was initiated by the main pulser, solenoid pulser; sequentially 

following by the kicker current pulser, the electron gun voltage pulser, and the data 

acquisition system. Except the RF signal diagnostic, the results to be recorded include the 

collector current, the solenoid current pulse, the kicker current pulse, and the electrongun 

voltage pulse during the experiment. When we seek the RF signal, we scanned the 

axial magnetic field in the design region, accompanied by a scan of the kicker current. 

The electron energy distribution was determined with the timing relationship between the 

electron gun pulse, axial magnetic field and kicker current. Attenuators were used at each 

experiment in order to protect the detectors. 

42

E-gun Voltage [kV] 

Current [A] 

15 

10 

5 

0 

1 

0.8 

0.6 

0.4 

0.2 

0 

(a) 

-20 0 20 40 60 80 100 120 140 160 

Time [us] 

(b) 

-20 0 20 40 60 80 100 120 140 160 

Time [us] 

Fig. 2.17. An electron gun voltage trace (a) and a single beam current trace (b). 

43

2.3. Experimental Results 

The 2D CRM-array experiment has been operated with one and two electron beams, 

as illustrated in Fig. 1.5b by dashed and solid curves, respectively. A single electronbeam 

in the center channel yielded the results shown in Figs. 2.18 and 2.19. The detector 

output trace is presented in Fig. 2.18a, together with the electron-beam energy trace. The 

frequency characteristic of the RF output signal is shown in Fig. 2.18b as measured 

during the pulse (the dots present the points of the measurement). The axial magnetic 

field in this run is 2.9 kG, which corresponds to a cyclotron frequency of 8.0 GHz. The 

current measured in the collector is ~0.1A. The average radiation frequency is 7.5 GHz, 

hence the device operates with a backward wave. This effect is clearly observed in Figs. 

2.18a,b by the curvatures of the voltage and frequency traces (note that in a backward 

wave interaction, the frequency decreases as the electron energy increases). A slightly 

higher electron energy results in a rabbit-ears shape of the detector output, as shown in 

Fig. 2.19. The optimal resonance in this tuning condition is satisfied below the maximum 

voltage. 

Single-beam measurements have been made in a wide range of axial magnetic fields 

and electron gun voltages. Oscillations were observed in different frequencies as shown 

in Figs. 2.20a-d. In all cases, the RF frequency tends to decrease as the electron energy 

increases. For axial magnetic fields in the range 2.6-2.9 kG (Figs. 2.20a-c), the 

corresponding wave frequency varies within 6.87-7.52 GHz, respectively, in the first 

passband of the periodic waveguide. For an axial magnetic field of 3.7 kG, interactions 

were observed in the second passband (9.75 GHz), as shown in Fig. 2.20d. In the second 

passband, the coupling is much smaller since the interaction occurs mostly with the 

second transverse mode, which has a null in the center. The emission in this case may 

result from the finite width of the electron beam, or from its slightly off-axis propagation. 

The CRM-array was operated also with a single electron-beam in the side channel. A 

typical result for a 2.7 kG magnetic field is presented in Fig. 2.21. The extracted power of 

the RF sample by the various couplers in all the single beam measurements was in the 

range of 5-25 W. This power level is sufficient for spectral measurements. 

44

Frequency [MHz] 

Detector output [mv] 

45 

30 

15 

0 

7,540 

7,520 

7,500 

7,480 

(a) 

60 90 120 

0 

150 

Time [us] 

(b) 

60 90 120 150 

Time [us] 

Fig. 2.18. Experimental results of the one-beam CRM oscillator at 2.9 kG: 

(a) the electron gun voltage (upper curve) and the detector RF 

output (lower curve), (b) the frequency variation during the pulse. 

45 

9 

6 

3 

E gun voltage [kV]



45 

30 

15 

0 

6,930 

6,900 

6,870 

6,840 

(a) 

40 80 120 160 

Time [us] 

(b) 

40 80 120 160 

Time [us] 

Fig. 2.19. An off-tuned operation at 2.7 kG: (a) the electron gun voltage 

(upper curve) and the detector RF output (lower curve), (b) the 

frequency variation during the pulse. 

46 

9 

6 

3 

0 

E gun voltage 

[kV]



6,890 

6,885 

6,880 

6,875 

7,100 

7,095 

7,090 

7,085 

(a) 

5.5 6.5 7.5 8.5 

Electron energy [keV] 

(b) 

5.5 5.7 5.9 6.1 6.3 6.5 


Fig. 2.20. Tuning characteristics of a one-beam CRM, at (a) 2.6 kG, (b) 2.7 kG. 

47



7,525 

7,520 

7,515 

7,510 

9,754 

9,753 

9,752 

(c) 

5.5 6.0 6.5 7.0 7.5 


(d) 

3.0 3.5 4.0 4.5 


Fig. 2.20. (Cont.) Tuning characteristics of a one-beam CRM, at (c) 2.9 kG, (d) 3.7 kG. 

48



450 

300 

150 

0 

6,930 

6,900 

6,870 

6,840 

(a) 

0 25 50 75 

Time [us] 

(b) 

0 25 50 75 

Time [us] 

Fig. 2.21. A 2D CRM-array operation with a single beam in an off-axis side 

channel at 2.7 kG: (a) the electron gun voltage (upper curve) and 

the detector RF output (lower curve), (b) the frequency variation 

during the pulse. 

49 

9 

6 

3 

0 

E gun voltage [kV]

The 2D CRM-array was operated with two electron beams as shown in Fig. 1.5b. 

Typical curves of the detector output and the electron gun voltage pulse are shown in Fig. 

2.22a. A frequency variation of the RF output signal is shown in Fig. 2.22b. The axial 

magnetic field in this run is 2.7 kG, which corresponds to a cyclotron frequency of 7.56 

GHz. The average radiation frequency is 6.9 GHz, hence the device operates again in the 

backward-wave regime. In a CRM operation with an electron-energy slightly higher than 

the optimal value, the synchronism condition takes place in the leading and trailing edges 

of the voltage pulse, as shown in Fig. 2.23. 

By increasing the axial magnetic field, the two-beam CRM oscillates also at 3.8 kG. 

Figs. 2.24a,b show the electron gun voltage, the detector output and the intra-pulse 

frequency variation in this case. The corresponding cyclotron frequency is 10.64 GHz 

and the radiation frequency is 6.7 GHz. This result was obtained without a kicker field. 

Comparing to the one-beam CRM experiments, in the two-beam CRM experiment, the 

cathodes have off-axis positions. Then the transverse magnetic field exists for both 

cathodes. The transverse velocity of the electrons for the CRM interaction in this case 

may result from the nature kicking of the solenoid magnetic field. 

A series of measurements were made in different electron gun voltages in axial 

magnetic fields of 2.7 kG and 3.8 kG (7.56 GHz and 10.64 GHz cyclotron frequencies, 

respectively). For 2.7 kG, the corresponding wave frequency is around 6.9 GHz, and the 

sampled output power by the probe is ~20 W. For an axial magnetic field of 3.8 kG, the 

interaction occurs around 6.7 GHz without a kicker, and the sampled output power is 

~6 W. Maps of RF-frequency vs. electron-energy accumulated in many runs are shown in 

Figs. 2.25a and b for 2.7 kG and 3.8 kG, respectively (note that each dot presents average 

values of the corresponding run). The electron energy acceptance for 2.7 kG is much 

larger than for 3.8 kG, presumably because of the smaller Doppler shift. 

50



90 

60 

30 

0 

6,865 

6,860 

6,855 

6,850 

(a) 

55 60 65 70 

Time [us] 

(b) 

55 60 65 70 

Time [us] 

Fig. 2.22. A two-beam CRM oscillator output at 2.7 kG: (a) the detector 

output (sharp curve) and the electron gun voltage (flat curve), 

(b) the frequency variation during the pulse. 

51 

9 

6 

3 

0 

E gun voltage [kV]



450 

300 

150 

0 

6,910 

6,880 

6,850 

6,820 

(a) 

0 30 60 90 

Time [us] 

(b) 

0 30 60 90 

Time [us] 

Fig. 2.23. An off-tuned operation of two-beam CRM oscillator: (a) the 

electron gun voltage (upper curve) and the detector output 

(lower curve), (b) the frequency variation during the pulse. 

52 

9 

6 

3 

0 

E gun voltage [kV]



180 

120 

60 

0 

6,900 

6,800 

6,700 

6,600 

(a) 

20 50 80 110 

Time [us] 

(b) 

20 50 80 110 

Time [us] 

Fig. 2.24. A two-beam CRM operation at high magnetic field, 3.8 kG: 

(a) the electron gun voltage (upper curve) and the detected 

RF output (lower curve), (b) the frequency variation. 

53 

12 

8 

4 

0 

E gun voltage [kV]



7,500 

7,000 

6,500 

6,000 

7,500 

7,000 

6,500 

6,000 

(a) 

0 4 8 12 


(b) 

54 

B0=2.7 kG 

B0=3.8 kG 

0 4 8 12 


Fig. 2.25. Maps of frequency vs. electron-energy accumulated in many runs 

around (a) 2.7 kG and (b) 3.8 kG magnetic fields (each dot 

represents the average of a single run).

2.4. Analysis and Discussions 

For the one-beam 2D CRM-array experiment, the agreement between the 

experimental results (Figs. 2.20a-d) and the theoretical tuning relation (Eq. 1.1 and Fig. 

2.15) can be evaluated by a mismatch parameter proposed as follows 

2 

⎡ β 0 ( ω) 

v0 

⎤ 

∆ = ⎢ ⎥ −1 

. (2.3) 

⎣ ω c − ω ⎦ 

This parameter is computed using the measured experimental data (i.e., the 

wavenumber ( ) 

β 0 ω , the total electron velocity 0 

55 

v , and the cyclotron frequency ω c are 

computed by the instantaneous em frequency, electron gun voltage and solenoid current, 

respectively). Eq. 1.1 and Eq. 2.3 teach that 

2 

( z ) v v ∆ ≅ ⊥ , where ⊥ 

v is the initial electron 

transverse velocity. Hence, the expected value for ∆ is in the order of one due to the 

actual v ⊥ induced by the kicker (note that v ⊥ is not measured in this experiment). Fig. 

2.26 shows the results of ∆ computed by Eq. 2.3 for the experimental runs presented in 

Figs. 2.20a-d, respectively. Negative values of ∆ in Fig. 2.26 can be attributed to the 

error range of the solenoid field measurement (~2 %), and to the high sensitivity of Eq. 

2.3 to the cyclotron frequency (note that ω ~ ω ). Nevertheless, a result of 

− 07 . < ∆ < 19 . indicates a reasonable agreement between experiment and theory. 

Delta 

2.5 

2 

1.5 

1 

0.5 

0 

-0.5 

-1 

(d) 

(b) 

3 4 5 6 7 8 9 


Fig. 2.26. The mismatch parameter ∆ (Eq. 2.3). The curves denoted a-d 

correspond to the results in Figs. 2.20a-d, respectively. 

c 

(c) 

(a)

The theoretical tuning condition of the CRM interaction (Eq. 1.1) and the Brillouin 

dispersion diagram of Fig. 2.15 are applied to analyze possible mechanisms for the 

resonant microwave radiation observed in the one- and two-beam 2D CRM-array 

experiments. The CRM tuning conditions observed in the one-beam 2D CRM-array 

experiment are illustrated in Fig. 2.27. The Brillouin diagram based on measurements 

shows the periodic-waveguide dispersion in the first and second passbands. The electronbeam 

lines are computed by Eq. 1.1 according to the experimental parameters for 

B 0 = 2.7 kG and 3.8 kG. The intersection points between the electron-beam lines and the 

waveguide dispersion curves indicate the em resonance frequencies. The results for the 

backward-wave interaction agree with the experimental results. 

The synchronism conditions observed in the two-beam 2D CRM-array experiment 

are illustrated in Fig. 2.28. Again, the Brillouin diagram (based on measurements) shows 

the periodic-waveguide dispersion. The electron-beam lines are computed by Eq. 1.1 for 

2.7 kG and 3.8 kG, and for electron energies of 6.5 keV and 10.2 keV, respectively. The 

intersection points between the electron-beam lines and the waveguide dispersion curves 

indicate the CRM resonance frequencies. One intersection point (at 2.7 kG) is in the fastwave 

region, whereas the other (at 3.8 kG) is in the slow-wave region. Both interactions 

occur with backward waves. In the first 2D CRM experiment with the two electrom 

beams, the CRM tuning results indicate clearly interactions with backward waves, and 

with fast and slow spatial harmonics of the periodic structure. The two-beam CRM 

interactions occur near the cutoff frequency of the first passband. The tuning condition 

for the fundamental harmonic interaction leads to a wide electron energy acceptance, as 

observed in this experiment (note the ~6 keV spread in Fig. 2.25a). 

These experiments provide some information on the multi-beam CRM spectral 

character. However, the multi-beam CRMs, which consisted of multi-beam electron 

guns, resonator systems, focusing magnets and collectors, are highly sophisticated 

systems due to the non-uniformity of the RF distribution in the cavity and the transverse 

contribution of the focusing magnetic field. One of the most difficult tasks is to develop 

an electron gun, which produces the multi-beam streams. 

56


14 

12 

10 

8 

6 

4 

d 

b 

2 

-160 -80 0 80 160 

c 

a 


Fig. 2.27. The one-beam CRM tuning diagram. The upper two curves show the periodic-waveguide 

dispersion in the first and second passbands. The lines present the electron-beam lines as the 

results from Eq. 1.1. The dashed curve indicates the fundamental mode of the rectangular tube. 

Slow 

Frequency 

[GHz] 

10.6 

10.2 keV 

9 6.5 keV 

Fast 

12 

7.5 

6 

-500 -300 -100 100 300 500 

Wave number [ 1/m] 

Fig. 2.28. A tuning-diagram presentation of Eq. 1.1 with the waveguide dispersion (Fig. 2.15), for the 

results of the two-beam CRM-array. The electron-beam lines, for 6.5 keV / 2.7 kG and 10.2 

keV / 3.8 kG, show CRM interactions with fast and slow backward waves, respectively. 

57 

3.8 kG 

2.7 kG

At present, we use the 2D simulation code, EGUN, commonly used in vacuum 

electronics, to design the multi-beam electron gun. However, these simulations do not 

obtain complete convergent results in the real systems, which lack 2D symmetry 

structures. The structure in the multi-beam electron gun is not the optimal focusing 

electrode, which arranges the uniform distribution of the current density in the multibeam 

device. Some improvement in the design of the multi-beam electron gun is 

necessary in the future since it will affect average power. To achieve this goal, it is 

necessary to use advanced 3D modeling codes to design the components in multi-beam 

CRM devices. 

2.5. Conclusions 

The spectral measurements show clearly the CRM interaction with backward spatial 

harmonics. Both, fast- and slow-wave CRM interactions are observed in the two-beam 

CRM experiment. The results of the two-beam CRM experiment show the feasibility of 

splitting the electron current to separate beams in the array. The same approach leads to 

the construction of advanced CRM-array experiments in our laboratory (2D and 3D 

arrays of five (carbon-fiber) and nine (thermionic) cathodes, respectively). The next 

challenge is probably to improve the RF output power of the multi-beam CRM devices. 

The complexity of the multi-beam design requires the development of advanced software 

and equipment, such as power supplies. However, those problems can be remedied. 

Specially, when 3D modeling codes become mature, they certainly will accelerate the 

development of the devices that lack 2D symmetry and alleviate the design difficulties 

for multi-beam CRMs. The optimism in multi-beam CRMs is based on current 

developments on 3D modeling codes and the spectral measurements in this work. 

Further studies proposed for the development of the multi-beam CRM-array concept 

[60] include (a) a radiation power extraction and efficiency measurements, (b) an 

investigation of coupling effects between several electron beams in a 2D array, (c) 

development of large 3D CRM-arrays, (d) studies of direct radiation from CRM arrays, 

and (e) active phased-array antenna features and radiation steering. 

58

Chapter 3 

The Carbon-Fiber CRM-Array Experiment 

This chapter presents the first experimental study of a carbon-fiber CRM-array. The 

CRM-array is operated here with the multi-beam cold-cathode array, made of a carbonfiber 

cathode array. According to our knowledge this is the first exploration of the multibeam 

cold-cathode array and its application in vacuum electronics. 

The next section, Section 3.1, describes the experimental design and setup of the 

carbon-fiber CRM-array. It includes the mechanical design of the device, a study of the 

multi-beam carbon-fiber cathode array, the design of the periodic waveguide and magnetic 

fields. In this part, the study of the multi-beam carbon-fiber cathode array is described 

intensively in the subsection 3.1.2. The fabrication of the carbon-fiber cathode is described 

first. Then, the experimental design and setup of the multi-beam carbon-fiber cathode 

array is presented. It includes the design of an electron-optic system of the multi-beam 

electron gun, a multi-channel pulsed power device, and an accelerating DC high voltage 

supply. The experimental results from the large area field emission “arrays” are given, and 

the general nature of voltage and current traces is presented. The effect of beam 

multiplication is discussed. 

The operation of the carbon-fiber CRM experiment is described in Section 3.2. The 

experimental results and discussions are presented in Sections 3.3 and 3.4, respectively. 

3.1. Experimental Design and Setup 

A photograph of the carbon-fiber CRM-array experimental device is shown in Fig. 

3.1. The oscillator tube consists of the electron gun with multi-beam carbon-fiber cathode 

array, a 2D periodic waveguide, a collector, a solenoid, and a kicker coil, which imparts 

initial transverse velocity to the electrons. The total length of the device is about 1.2 

meter. 

59

Fig. 3.1. Photograph of the carbon-fiber CRM-array experimental setup. 

60

A schematic diagram of the carbon-fiber CRM-array experiment is shown in Fig. 3.2. 

The electron beams are emitted from the multi-beam carbon-fiber cathode array, which is 

driven by a multi-beam electron gun pulser. Then, the multiple electron beams, in 

energies of less than 10 keV, are spun up by the kicker, injected into the corresponding 

channels in the 2D periodic waveguide, and interact with the em wave. The ignition of 

each cathode causes an abrupt fall in its voltage, down to around 1 kV during emission. 

The solenoid field is compensated by Helmholtz coils and five blaster resistors act as 

current limiters. The accelerating voltage between the grid and the anode is provided by 

the DC high-voltage source. The beam currents are monitored by Rogowsky coils. The 

periodic waveguide is terminated by half-period reflecting sections at both ends. 

The output signal is radiated from the exit plane of the waveguide to free-space, and is 

detected in the near-field by a horn antenna. The signal is attenuated and divided into two 

arms. In one arm, the signal is detected by a crystal detector (HP 424A) and recorded by a 

digital oscilloscope (Tektronix TDS 540). In the other arm, the signal passes a 4.7- 

5.3GHz bandpass filter (B.P.F.) in order to identify the frequency range of the RF signal. 

All data are collected by a computer using a HP VEE 3.0 (or Tektronix Wavestar) 

software. The experimental parameters are listed in Table 3.1. 

Although the carbon-fiber cathode can work at pressure above 10 -6 Torr, a better 

vacuum improves its operation. In this experiment, the tube is pumped down to a pressure 

around 10 -6 Torr. 

3.1.1. Mechanical Design 

An overview of the apparatus of the carbon-fiber CRM-array experiment is shown in 

Fig. 3.3. A 1.4 m high frame is used to assemble the apparatus in vertical orientation. The 

main vacuum chamber consists of a stainless steel vessel and a glass tube. The vessel has 

a 6 inch diameter, one 4 inch hole at the top and two 4 inch flanges on the side. The side 

sections are attached to a Varian 20 litre/s triode pump (model 911-5030) and a Varian 

Turbo-V250 pump. The top hole is attached to the glass tube, which has 10 cm diameter 

and 1 m length. An O-ring is used between the two parts in order to protect the vacuum. 

61

laster resistors 

multi-beam 

electron gun 

pulser 

carbon-fiber 

cathodes 

kicker 

grid 

anode 

periodic 

waveguide 

oscilloscope 

Fig. 3.2. Schematic of the carbon-fiber CRM-array experiment. 

Table 3.1. Experimental parameters. 

Electron beams: 

energy ~5 keV 

current per beam ~ 0.1 A 

pulse duration 0.4 ms 

number of beams 

Magnetic field: 

3 or 5 

solenoid ~2.4 kG 

kicker ~ 0.7 kA turns 

Periodic waveguide: 

rectangular tube 69 × 22 mm 2 

length 64 cm 

post diameter 2 mm 

post array 6× 20 

transverse periodicity 11.5 mm 

axial periodicity 30 mm 

62 

DC high 

voltage 

vacuum 

glass tube 

detector 

detector 

solenoid 

collector 

H.P.F 

attenuator 

splitter 

B.P.F 

antenna

vacuum 

glass tube 

solenoid 

periodic 

waveguide 

anode 

grid 

kicker 

carbon-fiber 

cathodes 

10 mm 

8 mm 

φ 100 mm 

Fig. 3.3. Apparatus of the carbon-fiber CRM-array experiment. 

63 

collector 

10.8 mm 

50 mm 120 mm 

50 mm 

630 mm 

220 mm 

4 inch flange 

6 inch flange 

Magnetic components 

Bronze copper 

Copper 

Stainless steel 

Glass 

Tungsten 

Ceramic 

O-ring

The periodic waveguide is assembled inside the glass. A horn antenna outside the glass is 

coupled to the interaction region inside (note that unless the glass is λ/2 thick, or its 

mismatch can be matched at both surfaces, the near field antenna may distort the radiation 

pattern or lead to frequency sensitivity due to multiple internal reflections [113]). The stalk, 

supported the electron gun and the periodic waveguide, has a length of about 28 cm. It 

consists of several stainless steel posts and disks. Ceramic pieces are used for insulation. 

Eight Tungsten feedthroughs are hermetically sealed into the glass. The high voltages are 

connected through these feedthroughs. High voltage probes, Rogowsky coils, and pulsed 

power supplies are installed in an adjacent rack mount. 

3.1.2. Multi-beam Carbon-fiber Cathode Arrays 

Explosive electron emission cathodes for microwave applications offer the potential to 

provide high efficiency electron guns due to larger current densities and direct 

modulations of emitted beams. This research is motivated by the desire to develop 

efficient, reliable and cost-effective multi-beam cathode arrays for multi-beam vacuum 

electronic devices, such as multi-beam CRM-arrays and low voltage, long wavelength 

multi-beam FEL arrays. The primary objective for this stage is to make an effective fivebeam 

carbon-fiber cathode array and explore the operation of multi-beam cold-cathode 

arrays in vacuum electronic devices. 

3.1.2.1. Experimental Configuration 

A schematic diagram of the multi-beam carbon-fiber cathode array experimental setup 

is shown in Fig. 3.4. The system consists of a multi-beam electron gun and a solenoid. 

The gun consists of two gaps. One gap is from five cathodes to a grid. This gap provides 

the electric field for the cathodes’ emission. The other gap is from the grid to an anode. 

This gap provides an acceleration of the electrons in order to increase the energy of the 

electrons for CRM interaction. The construction of the first section is similar to the 

electron gun construction described in Section 2.1.1. The accelerating gap, which avoids 

the need for a high electric field in the first section, and delays the breakdown of the 

system, is powered with a DC high voltage supply. The five cathodes are made of 

bundles of carbon fibers. Each bundle contains hundreds of fibers in a copper pipe (~2 

64

mm inner diameter). The diameter of each carbon fiber is less than 10 µm. The distance 

between two adjacent cathodes is 11.5 mm. The electrodes are placed inside a glass tube 

and are connected to the multi-channel electron gun pulser through the glass tube. The 

grid is located 8 mm ahead of the cathodes, and the distance between the grid and the 

anode is 10 mm. Both the grid and the anode are connected to Tungsten feedthroughs, 

which are hermetically sealed into the glass. The grid is connected to a ground potential 

outside and the anode is connected to a DC high voltage supply, which can provide up to 

20 kV DC voltage. 

The electron beams are emitted from the carbon-fiber cathodes, propagate in the two 

sections, and are collected by a metal plate. The collected current is measured by means of 

a 10 Ω resistor. The device is activated by a multi-channel electron gun pulser, a high 

voltage DC power supply, and a solenoid pulser. A Rogowsky coil (1:10 V/A) is used to 

monitor the output current from the electron gun pulser. Five blaster resistors, ~10 kΩ 

CuSO4 water resistors, are connected to the five cathodes in series separately and act as 

current limiters. High resistivity enables more tips to emit, and the magnitude of the 

emission from each cathode is more uniform. The emitter voltage, which is the potential 

between the cathodes and the grid, and the DC high voltage are monitored by two high 

voltage probes (Tektronix P6015A, 1:1000). All data are recorded by several digital 

oscilloscopes (Tektronix TDS 210), and collected in a computer by a Tektronix Wavestar 

software through GPIB cables. All cathodes testing are carried out with a base pressure 

around 10 -6 Torr, with and without an external magnetic field. 

high voltage 

probe 

multi-beam 

electron 

gun pulser 

blaster resistors 

carbon-fiber 

cathodes 

grid 

anode 

Fig. 3.4. Schematic of the multi-beam carbon-fiber cathode array experiment. 

65 

DC high voltage 

solenoid 

10 Ω 

collector 

vacuum 

glass tube 

oscilloscope

3.1.2.2. Cathode Fabrications 

The schematic of the carbon-fiber cathode is shown in Fig. 3.5. In Fig. 3.5a, the 

cathode consists of 10 µm bunches of fibers and a copper tube. During fabrication, a 

bundle of carbon fibers, contained hundreds of fibers, was trimmed (but not etched) and 

inserted by hands in the copper tube. The tube was mechanically pressed at the end in 

order to tighten the fiber bundle and to provide a proper electrical contact. An advanced 

scheme is shown in Fig. 3.5b. Comparing to the scheme in Fig. 3.5a, the cathode adds an 

electrical field shield around the tips of the carbon fibers. It improves the electrical field 

distribution for the cathodes’ emission. When a voltage is applied to the tube, the electric 

field created at the tips is magnified due to the extreme sharpness of the tips, which causes 

electron emissions. In many cases an electric field as low as 3 kV/cm is sufficient to 

produce plasma formation for electron emissions. A photograph of the cathodes is shown 

in Fig. 3.6. 

2 mm 

3 mm 3 mm 

(a) (b) 

Fig. 3.5. Schematic of a bunched carbon-fiber cathode (a) and 

an advanced scheme (b). 

Fig. 3.6. Examples of the end brush cathodes. 

66 

2 mm

3.1.2.3. Electron Trajectories 

The electron optics design of the multi-beam electron gun is performed with the 

EGUN code with a few assumptions. As in Section 2.1.1, we assumed that each beam has 

a perfect local symmetry around its own axis and the gap between cathode and grid (or 

grid and anode) is much smaller than the distance between two holes of the grid plate (or 

the anode plate). So simulating the center electron flow and simplifying the boundary, the 

code output for a 3mm carbon-fiber cathode with 8 mm cathode-grid gap and 10 mm 

accelerating section is shown in Fig. 3.7. Fig. 3.7a shows electron gun geometry and beam 

trajectory. It includes three regions: a cathode-grid region, a grid-anode region, and a 

beam tunnel. Fig. 3.7b and Fig. 3.7c present electron density versus radius and the angle 

of the electron motion measured from the z-axis, respectively. A magnetic field is used for 

the beam focusing. 

R (mm) 

Fig. 3.7. The EGUN code output for a 3mm carbon-fiber cathode, 

(a) the beam trajectory (radius (R) vs. axial length (Z)). 

67 

Z 

( mm)

Current density (0.119 A/mm 2 ) 

Fig. 3.7. (Cont.) The EGUN code output for a 3mm carbon-fiber cathode, (b) electron density vs. 

radius, (c) the angle of the electron motion measured from the z axis. 

68 

R 

( mm) 

R ( mm)

3.1.2.4. Power Supplies 

Three incorporating high voltage supplies for the multi-beam electron gun, 

accelerating section, and solenoid were used in the experiment of the carbon-fiber cathode 

array. The solenoid pulser is the same as described in Section 2.1.3. However, the multi 

channel electron gun pulser was redesigned in order to ensure the uniform current density 

of the multi-cathode array. Meanwhile, the DC high voltage was used for the accelerating 

gap. The design details are described in the section below. 

The multi-channel pulsed power system produces five separating pulses with fairly 

high voltages and output currents. The circuit is shown in Appendix B3. The pulser is fed 

by 220 V AC through a variable voltage transformer and a 10 A fuse. Then, this AC 

voltage is connected to a 220/460 V up-shift transformer. The output of the transformer is 

fed to five-channel charging circuits. Each channel consists of a low-voltage capacitor 

bank (C), a diode IN5408 that prevents a reverse recharging of the capacitor, and a 

transformer (car ignition coil). The charging voltage is monitored by a TY-43 digital panel 

meter. An SCR control circuit is used as a common gate. The five capacitors, about 10uF 

each, are charged with a rectified main voltage (600V), and then are discharged in an 

instant through the SCR and the ignition coils. The SCR is triggered by a function 

generator. 

The DC high voltage supply for the acceleration section was done in two schemes. 

Both of them used a modified Model 615 Pulserad power supply. The original Model 615 

Pulserad and our modifications are described in Appendix C. The circuits for both 

schemes are shown in Fig. 3.8 and Fig. 3.9, respectively. In Scheme 1, a long pulse is 

used to supply the accelerating stage. Compared to the electron gun voltage pulse, the 

duration of the pulse is much longer and it acts as a DC high voltage. A timing diagram in 

scheme 1 is shown in Fig. 3.10. In Scheme 2, the DC high voltage is coming directly from 

a charged capacitor bank in the modified Model 615 Pulserad. For safety, the capacitors 

are discharged after the shot of the electron gun. A corresponding timing diagram is 

shown in Fig. 3.11. 

69

CRM 

system 

1 kΩ 

1 kΩ 

Fig. 3.8. Circuit of a accelerating voltage source. 

Spark gap 

Spark gap 

50 kV pulse 

50 kV pulse 

20 kV 

1.5 kΩ 

1 µF 

20 kV 

1.5 kΩ 

1 µF 

Fig. 3.9. Circuit of a DC high voltage source. 

70 

PT-55 

Trigger amplifier 

High DC 

voltage supply 

PT-55 


High DC 


Control 

function 

panel 

CRM 

system 

Control 

function 

panel

Emitter voltage [kV] 


10 

5 

0 

-5 

-10 

5 

0 

-5 

-10 

0 100 200 300 400 

Time [us] 

Fig. 3.10. A timing diagram in Scheme 1. 

0 200 400 600 800 

Time [us] 

Fig. 3.11. A timing diagram in Scheme 2. 

71 

20 

15 

10 

5 

0 

20 

15 

10 

5 

Accelerating voltage [kV] 

Accelerating voltage [kV]

3.1.2.5. Electrical Performance 

The electron gun, which has one carbon-fiber cathode, was tested initially at a diode 

voltage of more than 4 kV (without accelerating voltage) with an 8 mm gap between the 

cathode and the grid. A ~100 mA diode current was observed. Then, increasing the 

number of the cathodes to three and five, the electron gun was tested in the same 

condition. Typical emitter voltage (or diode voltage) and current traces for a shot with the 

electron gun, which has five carbon-fiber cathodes, are illustrated in Fig. 3.12 (without an 

additional accelerating voltage). In this shot, the multi-channel gun pulser was adjusted to 

provide a more than 3 kV/cm electric field for each cathode. In Fig. 3.12, the emitter 

voltage rises rapidly (~2kV) during the first few microseconds. Then, the voltage drops 

sharply to ~500 V due to the impedance changing as the current turns on. After about 

450 µs there is a breakdown between the cathodes and the grid. This attributes to the 

property of explosive field-emission cathodes. Then the closure speed is about 1.8 cm/ms. 

The collector current was measured by a 10 Ω resistor placed between the collector and 

ground. A ~0.5 A current (total) was measured at the collector, that is about 0.1 A for 

each channel. The current density is around 1.4 A/cm 2 (7 A/cm 2 in the cathode-grid gap 

since we monitored the ~0.5 A input current for each cathode). Therefore, a long duration 

pulse dictates a low current density. The relative long rise time of the high voltage pulse 

caused the carbon fibers flare on a critical voltage. This may explain the long duration 

pulse with a low current density, relative to other one-beam cold-cathode researches. 

Adding an accelerating voltage, typical emitter voltage and current traces for a shot with 

five carbon-fiber cathodes are illustrated in Fig. 3.13. The pulse duration of the emitter 

voltage for a one channel is not significantly changed. So it seems that the accelerating 

voltage did not change the closure speed in the cathode-grid gap. 

Several shots were made with the modified Marx generator. In these experiments, the 

modified Marx generator connected directly with the five carbon-fiber cathodes. 

However, the emission was ceased in a very short time. Besides this limitation, the five 

cathodes could not be fired at the same time using the modified Marx generator, due to 

the non-uniformity of the cathode array. Therefore a special multi-beam pulse generator 

was built for the multi-beam carbon-fiber CRM array. 

72


5 

3 

1 

-1 

-3 

-5 

0 200 400 600 

0 

800 

Time [us] 

Fig. 3.12. A typical cathode voltage and current traces without an accelerating voltage. 

Emitter voltage [kV] and 

accelerating voltage [kV] 

5 

3 

1 

-1 

-3 

-5 

Accelerating voltage 

Emitter Voltage 

0 200 400 600 

0 

800 

Time [us] 

Fig. 3.13. A typical cathode voltage and current traces with an accelerating voltage. 

73 

5 

4 

3 

2 

1 

5 

4 

3 

2 

1 

Collector current [A] 

Collector current [A]

A series of measurements were made with the different number of the cathodes in 

similar condition. The influence of the number of beams on the breakdown of the system 

was checked. A typical experimental result of the electron gun with a single cathode is 

shown in Fig. 3.14. Figs. 3.14 a, b, c, and d represent the emitter voltage for a one 

channel, the accelerating voltage, the current at the collector, and the current at the 

accelerating gap, respectively. The corresponding experimental measurement of the 

electron gun with the five-beam cathode array is shown in Fig. 3.15. In this case, the 

appearance of a breakdown at the accelerating stage depends on the array density. The 

diode voltage for each channel in the experiment of the five-beam cathode array is similar 

to the voltage in the experiment of the one-beam cathode array. In a similar diode voltage 

for each cathode, when the number of cathodes increases, the effective accelerating 

voltage, which does not cause the breakdown of the system, becomes lower (~7 kV in 

Fig. 3.14b and ~3 kV in Fig. 3.15b, i.e. ~4 kV difference). Decreasing the input energy for 

each cathode, Fig. 3.16 and Fig. 3.17 show the observed results for the electron gun with 

one-beam and three-beam cathode array, respectively. Again, when the number of 

cathodes increases, the effective accelerating voltage becomes lower (~11 kV in Fig. 

3.16b and Fig. 3.17b without and with breakdown, respectively). But here the difference 

is much smaller, perhaps because the distance between two cathodes in the three-beam 

array is two times wider than the distance in the five-beam array. Comparing Fig. 3.14 

and Fig. 3.16, we also found that the effective accelerating voltage decreases when the 

diode-input energy increases in the same number of beams (7 kV in Fig. 3.14b and 11 kV 

in Fig. 3.16b). Therefore, the effective accelerating voltage is inversely proportional to the 

current density. In our configuration, the effective accelerating voltage for the electron 

gun with the three-cathode array is more than 7 kV; whereas, for the electron gun with the 

five-cathode array, the effective accelerating voltage is much smaller, around 3 kV. 

These tests are important because this is the first exploration of electron guns with multi- 

beam cold cathodes. It demonstrates that the ~400 µs multi-pulse with ~0.1 A for each 

channel can be produced with this configuration. We found that in similar diode voltage 

for each cathode, when the number of cathodes is increased, a lower effective accelerating 

voltage can be achieved, and the achieved effective accelerating voltage is decreased 

when the diode-input energy is increased in the same number of the beams. 

74

Emitter voltage 

[kV] 

Accelerating 

voltage [kV] 


Current at accelerating 

gap [A] 

4 

2 

0 

10 

5 

0 

2 

1 

0 

15 

10 

5 

0 

(a) 

(b) 

(c) 

(d) 

0 200 400 600 800 

Time [us] 

Fig. 3.14. An experimental measurements for a single cathode gun: 

(a) the emitter voltage, (b) the accelerating voltage, 

(c) the collector current, and (d) the current at the accelerating stage. 

75


[kV] 

Accelerating 

voltage [kV] 

Collector current 

[A] 

Current at 

accelerating gap [A] 

4 

2 

0 

6 

4 

2 

0 

2 

1 

0 

2 

1 

0 

(a) 

(b) 

(c) 

(d) 

0 200 400 

Time [us] 

600 800 

Fig. 3.15. An experimental measurements for a five-cathode gun: 

(b) the emitter voltage, (b) the accelerating voltage, 


76


Accelerating 

voltage [kV] 



gap [A] 

4 

2 

0 

15 

10 

5 

0 

2 

1 

0 

1 

0.5 

0 

(a) 

(b) 

(c) 

(d) 

0 200 400 

Time [us] 

600 800 

Fig. 3.16. An experimental measurements for a single cathode gun with a 

decreased input voltage: 

(d) the emitter voltage, (b) the accelerating voltage, 


77


[kV] 

Accelerating 

voltage [kV] 



gap [A] 

4 

2 

0 

15 

10 

5 

0 

2 

1 

0 

2 

1 

0 

(a) 

(b) 

(c) 

(d) 

0 200 400 600 800 

Time [us] 

Fig. 3.17. An experimental measurements for a three-cathode gun: 

(c) the emitter voltage, (b) the accelerating voltage, 


78

3.1.3. Magnetic Fields 

One of the major concerns about the multi-beam carbon-fiber CRM-array is the nonuniformity 

of the transverse contributions of the focusing magnetic field. A careful design 

of the solenoid was made to incorporate one main coil and two side coils. In this solenoid, 

the side coils were used to improve the uniformity near the edge of the magnetic field. 

Fig. 3.18 shows the cross section of the solenoid. The main coil was made out of a 2 mm 

diameter copper wire with 9.8 turns/cm. The two side coils were made out of a 2 mm 

diameter copper wire with 5 turns/cm. A large diameter kicker was designed in order to 

spin up the electrons. It was made out of a 1 mm diameter copper wire with 32 loops/cm. 

The final design of the kicker can be made in two ways. One method is to insert an array 

of thin, trim coils in the vacuum chamber, in order to produce the uniformity of transverse 

fields for each beam. The second method concerns the electrostatic effect. That means 

using the electrode structure to change the electrostatic field around cathodes. In the final 

off-axis design it may have a small difference in the electric field on the two sides of the 

electron beams. This could be designed by purposely inserting an asymmetric metal piece. 

The axial magnetic field at any point of the solenoid is calculated by Eq. 2.1. The 

result of the computer simulation is given in Fig. 3.19. In Fig. 3.19, the magnetic field of 

the main coil is shown by the dash-dot curve, the magnetic fields of the side coils are 

shown by the two small dashed curves, and the magnetic field of the solenoid is shown by 

the solid curve. The star sign represents the front position of the cathodes. In principle, the 

off-axis magnetic field of the solenoid can be calculated using the formulas or special 

software. In the experiment, a Gauss meter was used to check the magnetic field 

uniformity near the edge of the solenoid [114]. The parameters of the solenoid and the 

kicker are shown in Table 3.2. 

Fig. 3.18. Solenoid in cross section. 

79 

z 

B

Fig. 3.19. The magnetic field of the solenoid. 

Table 3.2. The parameters of the solenoid and the kicker. 

Parameter Main coil Side coil Kicker 

Turns 780 15 98 

Current [A] 100-200 100-200 20-140 

Inner radius [cm] 5.7 6.1 7 

Outer radius [cm] 6.1 6.3 7.4 

Length [cm] 80 3 3.5 

80

3.1.4. The Periodic Waveguide 

A photograph of the periodic waveguide is shown in Fig. 3.20. The waveguide 

consists of a metal-post array with 6x20 elements and is terminated by half-period 

reflecting sections in both ends. Figs. 3.21a and b show the measured resonant absorption 

and transmission peaks corresponding to the axial modes of the cavity at the first and 

second passbands, respectively. The resonances were measured by looking at the 

reflection coefficient (upper traces in Fig. 3.21 a, b) of the slow wave structure over the 

appropriate frequency range, as described in Section 2.1.4. The waveguide dispersion is 

shown in a Brillouin diagram in Fig. 3.22, as results from the measurements of the 

waveguide reflection and transmission coefficients. These intersections are shown by the 

dots in Fig. 3.22. The electron beam line is added to Fig. 3.22 in order to demonstrate 

CRM interaction in the first passband. The point a, which is the intersection of the 

electron beam line and the waveguide dispersion curves, indicates a possible CRM 

interaction with backward wave. Forward and backward wave interactions (β > 0 and 

n 

β n < 0 , respectively) differ by the tendency of the latter to act as absolute instabilities, 

and to oscillate (as observed in this experiment). The backward wave interaction could be 

the desired mode for a CRM-array oscillator. In amplifier schemes, however, parasite 

backward-wave interactions can be eliminated by a proper tuning to a tangential (grazing) 

point in Fig. 3.22. 

Fig. 3.20. Photograph of the periodic waveguide. 

81

(a) 

Fig. 3.21. The measured reflection and transmission curves at the 

first passband (a) and the second passband (b). 

82 

(b)


10 

8 

6 

4 

2 

a 

-105 -64 -23 23 64 105 


Fig. 3.22. The measured Brillouin diagram of the 2D periodic 

waveguide. The dashed line represents Eq. 1.1 in a 

cyclotron frequency at 6 GHz. 

83

3.2. Experimental Operation 

Each experiment began with a pre-running period to activate the cathodes. We found 

the following break-in procedure is useful. First, the cathode is under vacuum for several 

hours before firing them. Then, the operation is begun at the minimum voltage required to 

initiate the emission. After few tens of shots, the change of the gas pressure coursed by 

the cathode emissions should be reduced, compared with the first shots. Meanwhile, the 

accelerating voltage is increased in gradual until the desired voltage is achieved. In order 

to reduce the surface contamination, to stabilize the pressure and field emission currents, 

it is necessary to wait enough time between two shots. 

A control trigger system was used with function generators. The system connection is 

shown in Fig. 3.23. The main trigger comes from the solenoid pulser. Then it is sent to 

three function generators. After some delay, three trigger signals come out from the 

function generators and are sent to the gun pulser, kicker pulser and the 615 MR Pulserad 

control panel. 

Solenoid Pulser 

Trig. 

Gun Pulser 

Trig. Trig. TTL output 

Kicker Pulser 

Trig. Trig. TTL output 

Control panel of 

Function generator 

615 MR Pulserad 

EXT. Trig. Trig. TTL output 

Fig. 3.23. The trigger system. 

84 

Function generator 

Function generator


A typical experimental result of the three-beam carbon-fiber CRM-array is shown in 

Fig. 3.24. The emitter voltage of the center carbon-fiber cathode is shown in Fig. 3.24a. 

The accelerating voltage is shown in Fig. 3.24b. The cathode input current, measured by a 

Rogowsky coil, is shown in Fig. 3.24c. The microwave radiation output, detected through 

a 4.7-5.3 GHz bandpass filter, is shown in Fig. 3.24d. The axial magnetic field in this run 

is 2.4 kG, which corresponds to a cyclotron frequency of 6.8 GHz, hence the device 

operates in the backward-wave regime. 

Another radiation burst, observed with a similar magnetic field in the three-beam 

carbon-fiber CRM-array, is shown in Fig. 3.25. The emitter voltage of the center channel 

carbon-fiber cathode is shown in Fig. 3.25a. The accelerating voltage and the detector 

output are shown in Fig. 3.25b and Fig. 3.25c, respectively. A slightly higher electron 

energy (~8kV accelerating voltage) results in a three-peak shape of the detector output, as 

shown in Fig. 3.26c.The burst in center did not pass a 4.7-5.3 GHz bandpass filter and it 

may be caused by noises. However, the two side peaks of the signal passed through the 

4.7-5.3 GHz bandpass filter. 

Fig. 3.27 shows a typical case observed in the experiment. After the radiation burst is 

detected, a breakdown occurs at the accelerating stage. Fig. 3.27d shows the breakdown 

current. A series of measurements were made in similar conditions with three electron 

beams. The output power in the receiving antenna attains ~5 W. 

The multi-beam cold-cathode CRM-array was also operated with five carbon-fiber 

cathodes. Bursts were observed as shown in Fig. 3.28 and Fig 3.29. However, these bursts 

could not pass the 4.7-5.3 GHz band pass filter. Meanwhile, we observed the breakdown 

current, which started at the same time with the bursts at the accelerating stage. Therefore, 

these bursts may be caused by the breakdown and they are not the same as those in Fig. 

3.27. 

85

Accelerating 

voltage [kV] 

Current [A] 

RF detector 

output [V] 

Cathode voltage [kV] 

10 

10 

8 

6 

4 

2 

0 

0.1 

0.08 

0.06 

0.04 

0.02 

0 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

8 

6 

4 

2 

0 

(a) 

(b) 

(c) 

(d) 

0 100 200 300 400 500 600 

Time [us] 

Fig. 3.24. Typical experimental measurements for a three-beam CRM at 2.4 kG: 

(a) the carbon-fiber cathode voltage, (b) the accelerating voltage, 

(c) the cathode input current, (d) the RF detector output. 

86

Detector voltage [mV] 



100 

80 

60 

40 

20 

8 

6 

4 

2 

(a) 

0 

120 160 200 240 280 320 360 

Time [us] 

8 

6 

4 

2 

(b) 

0 

120 160 200 240 280 320 360 

Time [us] 

(c) 

0 

120 160 200 240 280 320 360 

Time [us] 

Fig. 3.25. An experimental measurements for a three-beam CRM: 


(c) the RF detector output. 

87 

400 

400 

400 

400


Accelerative voltage 

[kV] 

Detector output [V] 

4 

3 

2 

1 

0 

12 

10 

8 

6 

4 

2 

0 

1 

0.8 

0.6 

0.4 

0.2 

0 

(a) 

190 230 270 310 350 390 

Time [us] 

(b) 

190 230 270 310 350 390 

Time [us] 

(c) 

190 230 270 310 350 390 

Time [us] 




88


[kV] 




stage [A] 

8 

6 

4 

2 

0 

0.50 

0.40 

0.30 

0.20 

0.10 

0.00 

8 

6 

4 

2 

4 

3 

2 

1 

0 

(a) 

(b) 

(c) 

(d) 

0 

100 200 300 400 

Time [us] 



(c) the RF detector output, (d) the current breakdown at accelerating stage. 

89



4 

3 

2 

1 

0 


[kV] 

0.6 

0.4 

0.2 

0.0 

6 

4 

2 

0 

(a) 

80 120 160 200 

Time [us] 

(b) 

80 120 160 200 

(c) 

Time [us] 

80 120 160 200 

Time [us] 

Fig. 3.28. An experimental measurements for a five-beam CRM at 2.1 kG: 



90




4 

2 

0 

4 

2 

0 

0.80 

0.60 

0.40 

0.20 

0.00 

(a) 

80 120 160 200 

Time [us] 

(b) 

80 120 160 200 

Time [us] 

(c) 

80 120 160 200 

Time [us] 

Fig. 3.29. An experimental measurements for a five-beam CRM at 2.1 kG: 



91

3.4. Discussions 

Considerable progress has been made during this experiment. However, there were 

some difficulties with the multi-beam cold-cathode CRM-array. Beside the similar 

difficulties with the thermionic cathode CRM arrays we discussed in Chapter 2, the 

uniformity of the emission current was a major issue to deal with in the experiments. 

Since the field-emitted current is extremely sensitive to the value of the field at the emitter 

tip, and small changes in the anode-cathode separation could lead to large difference in 

emitted current for each cathode. In the beginning, we used single channel pulse generator 

to drive the multi-beam carbon-fiber cathode array. Although we tried to maintain 

parallelism between the anode and the separate cathodes, it was hard to get a uniform 

emission current since poor accuracy by this manufacture method. No matter how many 

times we changed the grid voltage, anode voltage, and adjusted the high resistive blaster 

resistor for each channel, we could not get five emission electron beams simultaneously 

for the most of shoots. Finally we built a five-channel pulse generator which has five 

separate output high voltage channels but with the same trigger system. By using this 

generator the uniformity was improved successfully. 

Another issue was the vacuum breakdown. As described in Section 3.1.2.4, the relative 

long rise time of the high voltage pulse caused the carbon fibers flare on a critical voltage. 

Since the high voltage (> 3kV) is necessary for CRM interactions, we need a high 

accelerating voltage between the grid and the anode. However, there was always 

breakdown when we add a large accelerating voltage at the beginning. During these CRM 

experiments, we used the break-in operating process for the multi-beam cold-cathode 

array. The process of operation consists of the following steps. First the accelerating 

voltage should be increased in gradual, then waiting enough time at each shot in order to 

reduce the surface contamination, to stabilize the pressure and field emission currents. 

This time is longer when the number of beams is increased in these experiments. 

Complying with this process, we have reached 7 kV accelerating voltage in the threebeam 

carbon-fiber CRM experiment. 

92

The theoretical tuning condition of the CRM interaction (Eq. 1.1) and the Brillouin 

dispersion diagram of Fig. 3.22 were applied to analyze the three-beam carbon-fiber CRM 

experimental results. The CRM tuning condition indicates clearly that these interactions 

occurred with backward waves. 

Although we have successfully explored the multi-beam cold-cathode array in the 

experiment, some improvements need to be done in future. First, the cathodes for this 

research are fabricated in a very simply way. It will improve the performance if a Spindt 

type cathode would be used (a possible vendor offering this semiconductor process 

technology is NEC Corporation in Japan or MCNC in US [115]). Second, it is necessary 

to use relatively short pulse generators in order to prevent the breakdown, improve the 

flatness of the emitted current and increase the repetition rate. Third, some improvement 

in material, such as coating with Cesium iodide (CsI), may also helpful [103,104]. 

The experiments of the carbon-fiber CRM arrays have clearly demonstrated the 

principle of the multi-beam CRM scheme with the cold-cathode array, and explored the 

use of a multi-beam cold-cathode array in vacuum electronic devices. The multi-beam 

cold-cathode array which is based on commercial carbon fibers was used as an electron 

source and produced a multi-channel ~400 µs long pulse. In the carbon-fiber CRM-array 

experiments, the three-beam CRM-array operated at low voltages, around 5kV, with a 

~0.4 ms pulse duration. Clear bursts of RF oscillations were observed around 5 GHz in 

this experiment. These experimental results show that it could be possible to use coldcathode 

arrays in multi-beam CRM devices in the near future. 

93

Chapter 4 

Conclusions 

The major objective of this study was to demonstrate, for the first time, a multi-beam 

CRM-array operation, and to study its features experimentally. The significance of the 

research is the experimental verification of the CRM-array conceptual feasibility, as a 

stage toward larger multi-beam CRM arrays. In addition, a secondary objective of this 

research was to explore the multi-beam CRM device using cold-cathode arrays and to 

develop an efficient, reliable and cost-effective multi-beam electron source. 


In the experimental study with thermionic cathodes, CRM oscillators were operated in 

a 2D scheme with one and two low-energy electron-beams (

Clear bursts of RF oscillations are observed around 5 GHz in the experiment. The 

experimental results show that it is might possible to use cold-cathode arrays in multibeam 

CRM devices in the near future. 

4.2 Suggestions for Future Work 

These experiments provided a preliminary investigation of the multi-beam CRM-array, 

and a good starting point for future experimental studies of large-scale multi-beam CRM 

arrays, and multi-beam cold-cathode arrays. The next challenge is probably to improve the 

RF output power of the multi-beam CRM devices. The implementation of this goal 

requires a careful design of the electron guns, and of the microwave components 

(preferably by advanced 3D codes). A full numerical simulation of the CRM array is 

essential, not only for a proper design but also for the analysis and optimization of the 

experimental results. 

Further experiments on larger arrays with a repetitive pulsed operation would be 

useful. The immediate repetitive operation for 2D CRM-array with thermionic cathodes 

can be designed and constructed. However, future improvement of RF power and 

operation with carbon-fiber CRM arrays will need relatively short pulse generators in 

order to prevent the breakdown, improve the flatness of emission current and increase 

repetitive rate. A potential limitation on the repetition rate with a carbon-fiber cathode 

array is the time required for the plasma to clear out of the gap. This time seems to be 

longer in these experiments when the number of beams is increased. It will improve the 

performance if Spindt type cathodes were used. A good processing for the carbon fibers 

will be also helpful since the material coating can reduce the closure speed. In order to 

decrease the closure speed, some improvement in material, such as coating with Cesium 

iodide (CsI), may be helpful. 

A consequent 3D CRM-array experiment that employs a 3×3 thermionic cathode array 

is under construction and operation in our research group by other researchers, and studies 

of direct radiation from CRM arrays, active phased-array antenna features, and radiation 

steering will be carried out in foreseeable future. 

95

Appendix A 

Computer Programs and Simulations Documentation 

A1. The EGUN Code Simulation for the 2D CRM-array Experiment 

The electron gun design was performed with the EGUN code [108] in the 2D CRMarray 

experiment. The boundary used to model the electron gun which has a 5mm 

diameter cathode and 6 mm gap is shown in Table A1 and Fig. A1. The potential 1 

represents the cathode and the potential 2 represents the anode. 

Table A1. The data of the geometry. 

Potential 1 1 0 0 3 3 0 0 2 2 2 2 0 1 

X 0 2.5 2.5 25 25 25 25 25 25 3 3 0 0 0 

Y 0 0 0 0 0 1 1 6 6 6 40 40 40 0 

Potential 3 

Potential 1 

2.5 mm 

X 

6 mm 

Potential 2 

40 mm 

Fig. A1. The geometry used to model the e-gun in the 2D CRM-array 

experiment with a 5mm diameter cathode. 

96 

25 mm 

3 mm 

Y

The Data of File 

The EGUN code output for a 5mm cathode and 6mm gap (B~2.2 kG) in Fig. 2.4. 

&INPUT1 RLIM = 25, ZLIM = 40, NBND = 320, POTN = 3, 

POT( 1) = 1.0000E-01, 

POT( 2) = 7.0000E+03, 

POT( 3) = 1.0000E-01, 

MAGSEG = 0, IAX = 0, AQUAD = 0.0, CSYS = 1, 

MI = 3, SX = 7.50, SY = 4.69, SCALE =' ', 

PASS = 2, XR =0.9950, ERROR =0.1000E-02, TYME= 300.0, 

LSTPOT = 3, LSTMAG = 1, LSTBND = 1, INTPA = 0, POIS = 0, &END 

1 0 1 0.0000000 -0.9990000 

1 1 1 2.0000000 -0.9990000 

1 2 1 2.0000000 -0.9990000 

1 3 0 -0.4980896 0.0000000 

0 4 0 2.0000000 0.0000000 

0 22 0 2.0000000 0.0000000 

0 23 0 2.0000000 0.0000000 

3 24 0 0.9990000 0.0000000 

3 24 1 0.9990000 2.0000000 

3 24 2 0.0000000 -0.9990000 

0 24 3 0.0000000 2.0000000 

0 24 4 0.0000000 2.0000000 

0 24 5 0.0000000 2.0000000 

2 24 6 0.0000000 0.0010000 

2 23 6 2.0000000 0.0010000 

2 5 6 2.0000000 0.0010000 

2 4 6 2.0000000 0.0010000 

2 3 7 0.0010000 2.0000000 

2 3 38 0.0010000 2.0000000 

2 3 39 0.0010000 2.0000000 

97

2 3 40 0.0010000 0.0052147 

2 2 40 2.0000000 0.0052490 

2 1 40 2.0000000 0.0052795 

2 0 40 0.0000000 0.0053139 

0 0 39 0.0000000 2.0000000 

0 0 4 0.0000000 2.0000000 

0 0 3 0.0000000 2.0000000 

0 0 2 0.0000000 2.0000000 

888 

&INPUT5 START ='SPHERE', RMAX = 2.500, RAD = 0.2500E+05, MAXRAY = 

20, 

LSTRH = 1,UNIT =0.1000E-02 

NMAG=20, 

CR=35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35, 

CZ=0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,190, 

CM=3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,3000,30 

00,3000,3000,3000,3000,3000, 

&END 

98

A2. The Magnetic Fields Calculation for the 2D CRM-array Experiment 

The magnetic field at the 2D CRM-array experiment is caculated by Eq.2.1 [109]. 

The Matlab program follows: 

% Fig2-6mag.m 

% Magnetic field calculation for solenoid and kicker in the 2D multi-beam array 

experiment 

z=-0.2:5e-5:.8; %step 

u=4*pi*1e-7; %constant 

N1=120;N2=225*4; %turns 

Ik1=20*3.2;Ik2=20*7.16; %current 

r2=.065;r4=0.103/2; %Solenoid & Kicker parameters (inner diameter) 

r1=.055;r3=0.126/2; %Solenoid & Kicker parameters (outner diameter) 

l1=0.023;l2=.6; %length 

z2=-0.07/2+0.01-0.3; %shift 

z1=-0.09; 

%MAGNETIC FIELD (Kicker) 

Bk1=u*N1*Ik1/2/(r2-r1)/l1*((z+z1+l1/2).*log((r2+sqrt(r2^2+(z+z1+l1/2).^2))./ ..... 

(r1+sqrt(r1^2+(z+z1+l1/2).^2)))-(z+z1-l1/2).*log((r2+sqrt(r2^2+(z+z1-l1/2).^2))./ .... 

(r1+sqrt(r1^2+(z+z1-l1/2).^2)))); 

%MAGNETIC FIELD (Solenoid) 

Bs=u*N2*Ik2/2/(r4-r3)/l2*(((z+z2)+l2/2).*log ...... 

((r4+sqrt(r4^2+((z+z2)+l2/2).^2))./ ..... 

(r3+sqrt(r3^2+((z+z2)+l2/2).^2)))-((z+z2)-l2/2).*log ..... 

((r4+sqrt(r4^2+((z+z2)-l2/2).^2))./ .... 

(r3+sqrt(r3^2+((z+z2)-l2/2).^2)))); 

99

hold on 

plot(z,Bs,'b') 

hold on 

plot(z,Bk1,'r--') 

hold on 

title('Magnetic field=f(z)') 

xlabel('z (m)'),ylabel('B (tesla)') 

grid 

100

A3. The EGUN Code Simulation for the Carbon-fiber CRM-array 

Experiment 

The electron gun design was performed with the EGUN code [108] in the carbon-fiber 

CRM-array experiment. The boundary used to model the electron gun which has a 3mm 

diameter is shown in Table A2 and Fig. A2. The potential 1 represents the cathode, the 

potential 2 represents the grid, and the potential 4 represents the anode. 

Table A2. The Data of the Geometry. 

Potential 1 1 0 0 3 3 0 0 2 2 2 2 0 0 4 4 4 4 4 4 0 1 

X 0 1.5 1.5 25 25 25 25 25 25 3 3 25 25 25 25 3 3 25 25 0 0 0 

Y 0 0 0 0 0 1 1 8 8 8 9 9 9 19 19 19 21 21 40 40 40 0 

Potential 3 

Potential 2 

Potential 1 

1.5 mm 

X 

8 mm 

10 mm 

40 mm 

Fig. A2. The geometry used to model the e-gun in the carbon-fiber 

CRM-array experiment with a 3mm diameter cathode. 

101 

Potential 4 

25 mm 

3 mm 

Y

The Data of File 

The Hermannsfedt code output for a 3 mm carbon-fiber cathode in Fig. 3.7. 

&INPUT1 RLIM = 25, ZLIM = 40, NBND = 320, POTN = 4, 

POT( 1) = 1.0000E-01, 

POT( 2) = 4.0000E+03, 

POT( 3) = 1.0000E-01, 

POT( 4) = 12.0000E+03, 

MAGSEG = 0, IAX = 0, AQUAD = 0.0, CSYS = 1, 

MI = 3, SX = 7.50, SY = 4.69, SCALE =' ', 

PASS = 2, XR =0.9950, ERROR =0.1000E-02, TYME= 300.0, 

LSTPOT = 3, LSTMAG = 1, LSTBND = 1, INTPA = 0, POIS = 0, &END 

1 0 1 0.0000000 -0.9990000 

1 1 1 2.0000000 -0.9990000 

1 2 1 2.0000000 -0.9990000 

1 3 0 -0.9990000 0.0000000 

0 4 0 2.0000000 0.0000000 

0 22 0 2.0000000 0.0000000 

0 23 0 2.0000000 0.0000000 

3 24 0 0.9990000 0.0000000 

3 24 1 0.9990000 2.0000000 

3 24 2 0.0000000 -0.9990000 

0 24 3 0.0000000 2.0000000 

0 24 6 0.0000000 2.0000000 

0 24 7 0.0000000 2.0000000 

2 24 8 0.0000000 0.0010529 

2 23 8 2.0000000 0.0010529 

2 5 8 2.0000000 0.0010529 

2 4 8 2.0000000 0.0010529 

2 3 9 0.0010000 2.0000000 

2 4 10 2.0000000 -0.9990000 

102

2 22 10 2.0000000 -0.9990000 

2 23 10 2.0000000 -0.9990000 

2 24 10 0.0000000 -0.9990000 

0 24 11 0.0000000 2.0000000 

0 24 17 0.0000000 2.0000000 

0 24 18 0.0000000 2.0000000 

4 24 19 0.0000000 0.0024853 

4 23 19 2.0000000 0.0024853 

4 5 19 2.0000000 0.0024853 

4 4 19 2.0000000 0.0024853 

4 3 20 0.0010000 2.0000000 

4 3 21 0.0010000 2.0000000 

4 4 22 2.0000000 -0.9990000 

4 22 22 2.0000000 -0.9990000 

4 23 22 2.0000000 -0.9990000 

4 24 22 0.9990000 -0.9990000 

4 24 23 0.9990000 2.0000000 

4 24 38 0.9990000 2.0000000 

4 24 39 0.9990000 2.0000000 

4 24 40 0.9990000 0.0052185 

4 23 40 2.0000000 0.0052223 

4 22 40 2.0000000 0.0052261 

4 21 40 2.0000000 0.0052299 

4 20 40 2.0000000 0.0052338 

4 19 40 2.0000000 0.0052376 

4 18 40 2.0000000 0.0052414 

4 17 40 2.0000000 0.0052452 

4 16 40 2.0000000 0.0052490 

4 15 40 2.0000000 0.0052528 

4 14 40 2.0000000 0.0052567 

4 13 40 2.0000000 0.0052605 

103

4 12 40 2.0000000 0.0052681 

4 11 40 2.0000000 0.0052719 

4 10 40 2.0000000 0.0052757 

4 9 40 2.0000000 0.0052795 

4 8 40 2.0000000 0.0052834 

4 7 40 2.0000000 0.0052872 

4 6 40 2.0000000 0.0052910 

4 5 40 2.0000000 0.0052948 

4 4 40 2.0000000 0.0052986 

4 3 40 2.0000000 0.0053024 

4 2 40 2.0000000 0.0053062 

4 1 40 2.0000000 0.0053101 

4 0 40 0.0000000 0.0053139 

0 0 39 0.0000000 2.0000000 

0 0 4 0.0000000 2.0000000 

0 0 3 0.0000000 2.0000000 

0 0 2 0.0000000 2.0000000 

888 

&INPUT5 START ='SPHERE', RMAX = 2.000, RAD = 0.2000E+05, MAXRAY = 

-20, 

LSTRH = 1,UNIT =0.1000E-02 

NMAG=20, 

CR=50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50, 

CZ=-20,-10,0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170, 

CM=1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,1500,15 

00,1500,1500,1500,1500,1500, 

&END 

104

A4. The Magnetic Fields Calculation for the Carbon-fiber CRM-array 

Experiment 

The magnetic field at the Carbon-fiber CRM-array experiment is caculated by Eq.2.1 

[109]. It is a little different with Section A2, since the solenoid consists of three coils. The 

Matlab program is as follows: 

whitebg 

clc 

clear 

hold off 

% Magnetic field of 5-beam CRM-array 

z=-0.1:5e-5:.9; 

u=4*pi*1e-7; %air permability 

%Solenoid & Kicker parameters 

N1=15;N2=390*2;N3=15; %turns 

Ik1=20*8.24;Ik2=20*8.24;Ik3=20*8.24; %currents 

r2=.1265/2;r4=0.1225/2;r6=0.1265/2; %external radius 

r1=.1225/2;r3=0.1143/2;r5=0.1225/2; %inner radius 

l1=0.03;l2=.8;l3=0.03; %length 

z1=-(0.028+0.015); %center of sidecoil1 

z2=-0.4; %center of solenoid 

z3=-(0.8-0.028-0.015); %center of sidecoil2 

%MAGNETIC FIELD (side coil1) 



(r1+sqrt(r1^2+(z+z1-l1/2).^2)))); 




(r5+sqrt(r5^2+(z+z3-l3/2).^2)))); 

105

%MAGNETIC FIELD (Solenoid) 

Bs=u*N2*Ik2/2/(r4-r3)/l2*(((z+z2)+l2/2).*log((r4+sqrt(r4^2+((z+z2)+l2/2).^2))./ ..... 

(r3+sqrt(r3^2+((z+z2)+l2/2).^2)))-((z+z2)-l2/2).*log((r4+sqrt(r4^2+((z+z2)l2/2).^2))./ 

.... 

(r3+sqrt(r3^2+((z+z2)-l2/2).^2)))); 

B=Bk1+Bs+Bk3; 

plot(z,B,'k') 

hold on 

plot(z,Bs,'k-.') 

hold on 

plot(z,Bk1,'k--') 

hold on 

plot(z,Bk3,'k--') 

hold on 

title('Mag.field=f(z)') 

xlabel('z (m)'),ylabel('B (tesla)') 

grid 

z=0.04; 




(r1+sqrt(r1^2+(z+z1-l1/2).^2)))); 




(r5+sqrt(r5^2+(z+z3-l3/2).^2)))); 

%MAGNETIC FIELD (Solenoid) `shifted .25` 

Bs=u*N2*Ik2/2/(r4-r3)/l2*(((z+z2)+l2/2).*log ...... 

((r4+sqrt(r4^2+((z+z2)+l2/2).^2))./ ..... 

106

(r3+sqrt(r3^2+((z+z2)+l2/2).^2)))-((z+z2)-l2/2).*log ..... 

((r4+sqrt(r4^2+((z+z2)-l2/2).^2))./ .... 

(r3+sqrt(r3^2+((z+z2)-l2/2).^2)))); 

bb=Bk1+Bs+Bk3 ; 

plot(z,bb,'r*') % 

set(gca,'XLim',[-0.1 0.9])% 

set(gca,'yLim',[0 0.25])% 

107

Appendix B 

Circuits of the Pulsed Power Devices 

Fig. B1. Circuit of the gun-solenoid pulser. 

108

Fig. B2. Circuit of the kicker pulser. 

109

Fig. B3. Circuit of the multi-channel gun pulser. 

110

C1. Model 615 MR Pulserad 

Appendix C 

The Modified Marx Generator 

The Model 615 MR Pulserad is an electron-accelerator system designed specifically 

for high-power magnetron experiments by Physics International Company. It consists of 

five subassemblies: (1) a DC power supply and controls, (2) trigger amplifiers, (3) a Marx 

generator, (4) a pulse clipping switch (crowbar), and (5) a high-voltage vacuum bushing 

(diode) [116]. 

Two trigger amplifiers mounted outside the pulser tank provide the high-level signals 

required to trigger the Marx generator and the crowbar switch. The trigger systems are 

comprised of a PT-70 control panel and a PT-55 trigger amplifier. 

Two inputs are required for these trigger operations: (1) a 7 kV DC bias and (2) a 

positive 300 V trigger. These inputs are supplied at the control console. The output of the 

trigger amplifier is a positive 50 kV pulse with a risetime of ≤ 10 ns and a duration of 

about 50 ns. 

External synchronization can be applied to the control function panel but must meet 

the following requirements: (1) ≥ +10 V, (2) ≤ 10 ns risetime, and (3) a pulse width of 50 

to 100 ns. 

The Pulserad 615 MR Marx generator consists of 6 energy storage "stages". In 

addition to a 0.5 µF high voltage capacitor, each stage also consists of some resistors and 

a spark gap which is pressurized with SF6. All the capacitors in the circuit are charged in 

parallel by the high voltage DC power supply. When the capacitors have been charged to 

the desired voltage level, the first stage is triggered by PT-55 trigger amplifier. This 

trigger pulse, which must exceed the breakdown strength (as low as 3 kV/mm) of the 

111

Marx gas in use (typically Nitrogen), causes the dielectric gas in the first stage to 

breakdown and become ionized (and thereby conducting). This effect causes the potential 

across the second stage gap to be twice the charging voltage. When all the spark gaps 

breakdown, the capacitors become connected in series across the load. Each capacitor is 

shunted by isolation resistors. Ignoring the losses in the isolation resistors and series 

resistive drops, the output voltage of the generator is six times of the DC charging 

voltage. A 12.5 Ω series-damping resistor is placed between the Marx and the diode to 

minimize reversal when the crowbar switch is fired. 

C2. The Modified Model 615 Pulserad 

The modified Pulserad 615 MR Marx generator is composed of capacitors, spark 

gaps, and resistors electrically arranged as shown in Fig. C1. Since we need a moderate 

voltage (< 20 kV) and long duration pulse in the experiment, we use the capacitor bank to 

supply the high voltage without the energy storage "stages". A spark gap is used as a fast 

speed switch. A 1 kΩ series resistor is placed between the spark gap and output in order 

to protect the capacitors. 

CRM 

system 

1 kΩ 

1 µF 

50 kV pulse 

1.5 kΩ 

20 kV High DC 


112 

PT-55 


Fig. C1. The modified circuit in Model 615 MR Pulserad. 

Control 

function 

panel

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